That is certainly what I would recommend! Although, depending on the engineering masters desired, physics or chem might be more useful.
Math undergraduate to engineering graduate needs to be very carefully planned so that you take course work that adequately prepares you for engineering graduate study. Meaning that you probably need to take electives in physics and engineering during undergraduate. Industrial engineering may be an exception, if you study applied math with statistics and operations research electives in undergraduate.
Better to just go into college as an engineering major if you really want to study engineering. Many colleges are not that selective for engineering majors.
I don’t do well in chemistry but maybe I will get better. Software engineering looks appealing because I am a computer type of guy. I know how to use some softwares as well. So do you think it would be better to do math 4 years as a major if I can’t switch the first or second year to the type of engineering I want and do computer science for grad? And if the engineering masters desired is petroleum, mechanical, electrical, would chem/physics be more useful or is math fine? Also if its possible to do the 4 years math and computer science for grad, would math be more useful than chem/physics?__________“ucbalumnus” I applied to some colleges for engineering as well! 
I just applied for math for the colleges I barely reach because of their high engineering major demands.
Math maps best to computer science and industrial engineering and a few specialties of other fields.
Physics maps best to EE and ME and Aero.
Chem maps best to ChemE
Petro and Nuke split chem and physics pretty evenly.
So yes, math to comp sci would be doable. Regardless, ucbalumnus is absolutely correct when he says that you need to be careful selecting your coursework - if you don’t have some prep for your graduate field you will have a very hard time of it.
With your GPA and SAT scores, why do you think a Math major will be a good fit (unless you have a high Math sub score)?. IMHO, I think a pure math major is more difficult than an engineering degree. Completing a Math degree and attempting an Engineering MSE might present some severe challenges. You will more than likely have to spend a year to 2 years doing basic engineering courses before you can start taking graduate level engineering courses. The few people I know who have gone this route, simply did another undergraduate degree in Engineering and then an MSE. There are very few engineering schools which offer masters degree in Mechanical or Electrical engineering without an undergraduate degree in that discipline.
Pure math versus engineering entirely depends on one’s mindset. One is not inherently harder than others. I’d have a harder time in math but ice met mathematicians that really struggling doing anything “practical”.
That is a valid question, but it is the OP’s time and money. I graduated in the middle of my class (good SAT’s, though) and was predicted by my alma mater at enrollment to have a 46% chance of dropping out and only a 1% chance of making the Dean’s List - I fooled them all by doing both, and am now in a top grad program in my field. OP is not in a great position right now, but they can still pull it off if they work hard at it.
I know people who have gone from science undergrads directly into engineering grad programs, it happens all the time. It does certainly depend on the specialty, of course - in EE, getting into computational electromagnetics or RF or optics is pretty easy with a physics degree, while something like robotics or circuit design would be extremely difficult without the engineering undergrad.
Conversely, there are extremely few situations in which I would recommend a second undergrad degree to someone. They simply are not worth it 99% of the time. The only guy I knew who really needed to do it was doing a mid-life career change. Grad study rarely requires a broad background, indeed it is quite focused, so taking a few courses as a non-degree student is generally more than enough to make you an acceptable candidate. Heck, most programs expect a certain amount of catching up anyway, as few undergrads are really prepared for grad study in their specialty on day one. Besides which, a second undergrad usually means little or no funding, and why pay out of pocket for 4 years?
My problem is that I already submitted my application to some colleges as Mathematics major. 
However, I heard that they ask you again if math is really what I want to major in or do I want to switch once I am accepted, is that true? Or should I call the colleges up and change my major? According to you guys, going into math major would be foolish but I thought you barely do anything involving your major the first 2 years and you could switch easily. Now that I see what you guys are saying, I guess some people have mislead me with these false information. “Jamrock” I see what you mean; my math score wasn’t very high but it was my highest. 
@TrynaLearn Don’t stress too much about the SAT math, it’s an odd thing. I’d taken Calc I and II when I started college, had As in both, took Calc III my first semester, got an A in that - and my SAT math score was only 650, which was my lowest subscore. My sister got a 730 on math and she got As in the calc sequence as well - only difference was that her class averages were around 99% and mine were more like 96%.
You can do it, but because the engineering curriculum is very rigid and sequential, you will likely delay your graduation.