South Padre is nice but it's a REALLY LONG drive, like 6-8 hrs!! Not sure if your 78 yr old MIL will like the drive. Flying is easier but then you have to rent a car.
Galveston is nice and it's closer -- about a 4 hr drive. And where we were at -- the beaches were nice. in fact, I didn't see any bad part of the beach there. I think back in the 80s-early 90s -- galveston got a bad rap for their beaches... but they've cleaned them up and put up more enforcement/codes since then. unfortunately some natives still think that galveston looks the same way it used to - although they haven't visited it in years.
If you go farther south on Galveston island --it's less crowded and nicer. There are some beach homes there that you can rent that are right on the beach, and they are away from the crowds. We loved renting this house and being able to walk to the beach every day! It's a little drive to the main hub of Galveston city - but I liked being away from the noise, traffic and crowds.
http://www.bayreef.com/rental/rentals01.htm
Here is a link to some beach rentals in Galveston Island... i think we stayed on the Acapulco beach area. It's a really nice getaway! so peaceful! and we really enjoyed the beach!!!