You are in the 99th percentile out of the 1.84 million who took the ACT.
You are doing very well!
Still, as you are aware, it’s important to figure out your balance and honoring your commitments. Especially before our kids go off to be on their own, we parents like to see our kids showing that they are able to follow through on what they promise. There will be even more distractions when you are living on your own, far from your folks. Figuring out how to set and keep priorities is an invaluable skill and one that your parents will be thrilled for you to learn sooner than later.
Your stats would get you a 100% out of state tuition scholarship at the University of Alabama - Huntsville, which is pretty cool if you are considering a career in the STEM field.
Your stats will also get you a 100% tuition scholarship at Ole Miss (University of Mississippi). You’d also qualify for the Holmes Scholarship, which is an additional $3000/year. AND you’d qualify for the Academic Excellence Technology Award, which is a one-time $1000 scholarship. Go to http://finaid.olemiss.edu/scholarships/#8 for more info.
If you’re into foreign languages, they have excellent programs there in Chinese, German, and Arabic (along with scholarships for people with your stats, which will pay for all of your year + summer abroad fees).
Mom is being a total drama queen and playing the guilt game with you, my guess is this has been her m.o. for your entire life, just amp’d up for the college process. Show her you didn’t ruin anything by taking control of what you need to do to get to the school you want and can attend (academically and financially). You are getting a lot of good suggestions on making the most of merit money with those great scores.
You have to talk with your mother. Apologize for not ordering the books and say you’re ready to study.
However you need to explain you are better off applying with your 34 than with your SAT. Just submit your ACT. (Colleges want EITHER ACT OR SAT and if you submit your SAT you’ll have to submit all scores for superscoring). However I would still take the SAT in August - but sat subject tests. Retake math2 and take a non science subject to show academic breadth. English literature is fine if you’re good at analysis. Penn likes high subject scores (especially in math and they assume calculus).
Just an FYI, community college sounds like an idle threat to me. UNM would be cheaper - your stats would qualify you for full tuition if you were to start as a freshman there.
I took a look at some of your chance me threads and it sounds like you are also interested in other OOS publics. This may be where your parents are engaging in some legitimate pushback. For example, as an out of state student, FL is unlikely to provide much of a discount. It is a great flagship. But it is also overcrowded and has impacted majors. Your parents might be reluctant to pay extra for you to attend a different large public university but would perceive value added at a top 20 school that would justify the upcharge. As others have mentioned upthread, I would target OOS publics that appeal to you that also offer merit aid for high stats/test scores.
Have you heard if you made the cut for NMSF? That would also open merit chances at places like Northeastern (coop program might appeal) or USC(alifornia).
Bottom line - you have a great ACT, respectable SAT subject tests, strong and varied ECs and a GPA that might be a trifle low for top 20 schools but is within range for consideration. If there is still time, I think your application would be enhanced by retaking subject tests rather than an additional attempt of the SAT I. I believe it may be possible to change your registration on line to take the subject tests - you might want to look into it.
I would focus on writing killer essays. Your competitive prep school should have a top notch college counseling program - make full use of it to craft an appropriate list.
Just go on khan academy to practice.
It’s really hard to know what your mother thinks you are going to get out of the SAT that you don’t have from the ACT, but the best thing is to humor her and study for the SAT and take it. BUT, I think you should go ahead and take the ACT again (and again) in hopes of getting a 35 or 36. Contrary to what other say, I think a 35 is much more impressive than a 34 and a 36 is almost magical.
There are a number of schools that will offer tuition-plus based on a 34 ACT and a 3.5 grade-point. Some are automatic, while others are by application. Of the flagships, Ole Miss is probably going to be the most generous, followed perhaps by Alabama. These might not be the schools you are wanted to go to, but free is a really nice price. So just keep your options open and retake the tests.
Two things. First, there are many upper tier schools outside of New England or even in those states. Have to go to a state school or second tier school will not end you life. You will get the education for which you work. Second, our lives supposedly or ruined any number of times in you life Unless you do something very illegal and get your life very curtailed, there will be books to read writing, and lure.
There is nothing “magical” about any particular standardized test score. A score of 36 on the ACT will not get anyone into any school, just as a score of 34 will not keep anyone out.
Some kids do better on one test or the other. If you – or your mother – insist on your taking another standardized test, I’d retake the ACT as you did significantly better on it than you did on the SAT. That said, I think taking either again is a complete waste of time.
I say concentrate on the essays.
If you’re at a good prep school, follow the advice of your college counselor throughout the process. Also apply to UNM. You will undoubtedly get into some fine schools. At that point, if your mom still says she will only pay for UNM, you are stuck, but I really doubt that will happen with an acceptance to a more prestigious college in hand. Moms freak out sometimes. Ask my kids.
@twinsmama OP is definitely not stuck if mom will only pay for UNM. There are more options than what she has given, and it’s up to the OP to determine if any of them are more appealing than capitulating to mom’s terms.
Yes, your mother is overreacting. Yes, a 34 will get you in many great schools. But what sticks out to me is how easily you could have avoided this by keeping an easy-to,-complete promise and some relatively painless studying… What you and many others your age don’t seem to grasp is that you usually go through this undergrad application thing just once, and it really irks some of us when our kids decide that’s the perfect time to get blase’ , sloppy, and lazy about it. Few things can pay as much in dividends (both in acceptances & scholarships) than even a small jump in ACT/SAT.
good grief. A 34 is awesome. You have not ruined your life. I know that sometimes it gets stressful applying to colleges and thinking about the future but you rocked the ACT and will get into a lot of schools. Good luck. Take a deep breath and you will be fine. (and if your mom is like me maybe give her a glass of white wine.) 
34 is smokin’. You’ll be fine.
OP: You sound like an excellent candidate and a great kid. It is not at unusual for teenaged boys to spend too much time on video games, even very driven kids.
I would actually think it is better to cancel the August SAT than try to cram for it. Apologize to your mom and explain that the 34 ACT is equivalent to an almost perfect SAT score so you did not think taking it again was beneficial, but that you should have talked about it with her before making that decision.
I think your mom is frustrated and lashing out thinking you are not taking things seriously. However, you need to have a back-up plan. It is possible that you won’t get into a top 20 (although it seems like you have a decent chance). I would also talk to your guidance/college counselor about your chances and your issues with your mom (if she doesn’t come around) to get some schools where you would get good merit aid.
Good luck!
I agree your scores are fine. And that Mom is wrong about further SAT improvement being key.
BUT:
What’s with “would it be wise for me to send just my ACT or do most colleges want to see both?”
Have you researched what your targets ask for? If you don’t have a grasp of this now, and what will make you an interesting candidate (esp for highly competitive colleges,) you should get cracking.
All you’ve told here is the bare bones, not how your application will flesh out. The app and supps are a self presentation, not just a resume. If you don’t have some idea how to do this with savvy, you’re flying blind.
Maybe your parents can’t afford the expensive schools, or just don’t want to spend that significant amount of out-of-pocket money, and this is just preemptive excuse to steer you to a high merit award college.