what muscles / movements in the core are good for stabilizin

Sit-ups are excellent exercise if you can do them. That'll target your abdominal muscles mainly. Don't forget to do back and sides while you're at it to get even core strength. A good back exercise would be to sit at the edge of your bed and hold your wife's hand with her standing infront of you and try pulling her towards you while she resists. Do the same on the sides so have her pull on one arm while your try to dip to one side. Doing those on top of your ab workout will get you a nice strong core in no time!

It depends keithbruce, I suggest only doing certain exercises set up for you with a professional. I started with a P.T., then a gait trainer , and eventually a regular trainer who was a former P.T..
All of these people knew what muscles I could work without hurting myself. Once I regained strength in certain muscles I could work on others.
Not everyone has this option, but I'd at least only do what your doctor recommends.