B.C.
I think you are letting the emotion of the moment get the best of you. The kids can have fun in the hotel pool. The Alamo is real close. The riverwalk has boats that travel the river and should be fun for the kids. If you have trained your kids to hold your hands they should be managable for short stroll on the riverwalk. The riverwalk has benches so you can rest frequently as needed. Bring along a book or two to read to the kids. The story of the Alamo has been written about in kids books many times and should be of interest to the kids. The riverwalk at night has all kinds of lights that twinkle and should be of interest to the kids. If you stop at subway or McD or BL or Wendy's you should be able to get something cheap and easy to eat so the kids can have a picnic.
You are only limited by your imagination. But if your doctor has put you on bed rest you shouldn't go.
Good luck to you and yours.
If the room costs too much, then cut back on the restaurant meals so that Sea World becomes more affordable.