I have a 7, 5 and 3 yr old, and found the easiest thing with my little 'un was to stop carrying him before the op. I started just a few days before (my op was a cancellation) and if he wanted a cuddle or to sit on my knee, I told him to let me sit down first, then he climbed up. When I came home post-op, I showed him my dressing to remind him to climb up gently.
I don't know how effective this will be with a 2yr old - perhaps you could ask for help in the beginning.
After about a week, I had picked my son up (awkwardly) once and suffered for it - I had excruciating pain in my left side, so bad I couldn't straighten up for a day or two. Docs couldn't find anything else wrong, so it was put down to muscular. They have to cut through muscle which needs to heal as well as the obvious areas.
I know it's hard, but if you can get help for when you first return home, accept it.
Good luck