Mine's a permanent(birth defects affecting my right arm, have about 1/2 normal use, is shorter, weaker, hand at an odd angle), but even having it all my life, there are things I was not expecting to run into when it comes to being a mom. Basically anything that needs two hands, lol.
Diapers, especially the first few months when we used cloth, were really hard. Luckily I never had to handle my breast to latch DS, but when his head was supported by that arm, it would ache so bad because it's weaker from less use, but it's better now. Getting him in and out of babywearing gear and positions has always been crazy.
Our biggest weirdness so far was that the bar on the stroller we had was much too low, and wouldn't steer 1-handed. I had to lean forward to push it, and that was messing up my back. The solution; we got a wagon. That handle goes up and down depending on angle, so it fits anyone's height perfectly, and can be used one handed, and I can use either hand to pull it.
Basically, you need to work around it. If one thing isn't working, try it differently. If it still isn't working, look at the very roots of why it's not working, and try again.
Can't reach things? Move them lower. Can't carry things? Enlist the kids, starting with oldest. Need help, period? Make preparing the food a group activity.
You want to play with them without having to be very active, right? As long as you are active enough to keep healing, I see no problem with that. Try scavenger hunts. Make lists of the weirdest things you can think of, and see what they bring. Younger version: Ask them to go to their room, find the most interesting (if they know colors, sizes, shapes, use them!) say, green thing, bring it back, and tell everyone else why they picked that, what other green things there were, and why this was the most interesting to them. Coloring and reading are other things that can be done from the couch. Blowing bubbles if you have a bench outside would be good, or if outside isn't an option, out a window. You can see who's lasts the longest. Do something with dressing up and role-playing, like a play with no script. Something my son(20 months) likes to do is put all kinds of things on my scanner, then I tell the computer to scan it, even though it's wide open, and we look at the picture that comes up. Sometimes he moves things in mid-scan, and those turn out pretty cool. Something slightly more active, do a from-the-couch bean-bag toss, you can use small soft toys and a box. Have the kids put the box in a good spot, everyone pile on the couch, and take turns throwing.
I hope that helps, just remember, get to the very core of why something isn't working first, and you'll be able to come up with a different option faster. You can do this!