Hi GBC I am no expert in this area but can share with you what I was advised after my own mx, ANC and LD reconstruction two years ago...
Avoid any highly repetitive exercises (10 or 20 reps is OK, several sets of reps may not be) and never lift anything over 1.5kg above shoulder height on the affected side.
No push-ups, but the 'against the wall' version is OK. As you will guess, I was mortified not to be allowed to do full on push-ups.... not :-).
I have been told not to put my 'full' weight through my affected arm, but that said, once tripped over and used that arm to save myslef, with no ill effect. I have done the 'plank' which done properly will distribute your weight and use your abs to hold you up, but to be honest I wasn't entirely comfortable with doing it as it felt 'odd' in my reconstruction.
A pilates teacher really ought to be able to find out what is or is not safe for you to do, and adjust exercises accordingly.