@amiechoke I would highly consider retaking calc I. She only got a 4 on the AB test and while that is good it is a sign that there can be an improved foundation. If she is not able to master 100% of Calc I, then Calc II will be a killer since a lot of it is just grueling rule memorization that even I disliked when I took BC Calc. Take it from me and start with something easier (calc I) this fall versus jumping straight to Calc II. (FWIW I took the entire calculus sequence in high school so I know what I got myself into).
@atomicPACMAN07 I am counseling my kids to take Calc II again as Freshman. They took Calc BC and struggled with the Integration of trig functions and also series (L’Hopital, Taylor, Infinite). They should take these again because they started to catch on pretty good at the end of this (spring) semester.
@amiechoke I agree with @atomicPACMAN07 that your D should take Calc I again because it will be a good refresher and she has not taken Calc in a whole year. Calc II is pretty much memorization and rule application. It surely is not a class you want to start with unless you have had some previous exposure.
I did ask two professors at UA, ME and Chem E, via e-mail that my kids would have credit for Calc I and II and both said they should start with Calc II as a refresher. That pretty much sealed the deal for me.
Well put @CyclonesGrad thanks for your input on the matter 
Calc II is one of those subjects that people either make it or not and tells them ideally if difficult STEM majors are for them (engineering, physics, etc). I won’t lie that Calc II was difficult and awfully tedious but with the right amount of effort it can be accomplished. I only ever recommend people skipping calc II to go onto calc III is if 1) they got a 5 on the AP BC Calc test 2) and they got A’s both semester of their BC Calc test. At that point it becomes purely preference to move on confidently or not. I didn’t find issue moving onto Calc III and DFQ so it worked out for my case. It’s all relative.
@atomicPACMAN07 I totally agree that you need to have aced both semesters of AP Calc BC to move to Calc III in college. I will say that Calc II is pretty much memorization with not a lot of intuitive connection. What it really teaches is how to breakdown issues into finite pieces that can be solved. If you work enough problems, you eventually catch on.
The difference between those that do and those that do not struggle with Calc II is that some are visualization thinkers (struggle) and some are memorizers (do not struggle) The interesting thing is that the visualization thinkers do well in Physics and Statics/Dynamics (can picture what is happening and apply formula).
Overall, the most successful engineering students are visualizers that then apply the equations to the situation. That is really what engineering is about. That is why many struggle so mightily with Calc II. Surviving that class is key because the following classes will be easier.
More than anything @CyclonesGrad it’s mostly about endurance. It is difficult for some to put in the amount of effort it requires to have a solid foundation of calculus, whether it be with memorization and/or tedious homework practice. I didn’t find calculus overall to be difficult because everything concept wise built off each other and I could use my interest in physics to reinforce concepts of derivatives and integration to real world concepts. I think calculus is a great weed out class since it sets the tone for getting into more abstract and difficult concepts that some may not want to endure in. That’s why for some it’s important to get as much practice as possible to be prepared, whether that be taking the class again or not.
Calc II is traditionally a bear at UA (not sure if it’s that way at most schools) and harder than Calc III. My son had to start from the beginning of the calculus sequence because he didn’t have AP credits. He’s a very strong math student and had the equivalent of BC his senior year, so he was well prepared. He aced all three sections (including the honors version of Calc I), but he said Calc II was a lot more demanding than I or III.
If your twins are strong math students and earned 5s on their AP exams, @CyclonesGrad, I’d suggest they take credit for I and II and go straight to III.
@amiechoke, I think your approach is the wise one for your student, based on what the engineering department advises and what I’ve witnessed from a range of students over the years as well.
Like @LucieTheLakie advised that it’s a good idea to take the credit if you feel confident. Bama is extremely generous with AP credit for a reason. Don’t take more classes than you absolutely feel it necessary.
Agree with @LucieTheLakie
Based on what my son and his roommates say, Calc 3 at UA is easier than calc 2.
Thanks very much for replies, all. BTW I can’t find the discussion clarifying this but can her 4 in AP Calc still be of any use to her if she is taking Calc I for credit?
@amiechoke if you have a 4 on AP calc AB and you decide to take calc 125, you forfeit your AP credits.
@SouthFloridaMom9 Do you mind posting who your DS had for Calc 1? You mentioned that he had a tougher professor so I would like DS to avoid him/her.
@bandmomof3 - he’s taking Calc 1 through University of Florida online dual enrollment. I can message you the professor if you still want it. He’s been holding his own. After watching him wind through the semester I think the prof and the TA are pretty decent. The material is tough in an online format. But again, he’s hanging in there. Final next week! 
For what it’s worth: some of the best Calculus professors are Gibson, Zhao, Liem, Hisa, Chen, Song and Trace. Trace though seems to be love-or-hate, people say he really emphasizes theory and has a tendency to go on tangents about it.
Thanks @SouthFloridaMom9 ,I think he’ll pass on UF online course. Thanks @Mandalorian I’ll pass on the information to him