Hi Kathy,
I don't know whether U of P or AIU require you to obtain permission to take other classes while enrolled, but some colleges do. However, my opinion is that it might be better not to work on two Bachelor's degrees simultaneously.
Have you considered getting a degree in Software Engineering or something similar and taking web design courses as electives? You might be able to cover much of the same ground without the additional time and cost involved in getting two degrees.
If you really want both degrees, I think it would be better to do them consecutively. You would probably finish both in about the same time, but you would have one much sooner. And you may decide after a few years that you need a break from college for a while... if you were working on two degrees simultaneously, you might still have a significant amount of work to do to get either at that point. The only advantage I can think of to doing both at once is that it's more likely that you would be able to keep the pipeline full, so to speak, by having a larger number of courses available to schedule each semester.