I'm going to tell my wife that she will need to take time off work when the babysitter isn't available.
Why wouldn't you babysit your kids?
I need to work so my wife will need to watch the kids.
I get that you need to work, but apparently your wife has a job too. You can't place all the childcare responsibilities on just your wife. Try working out an alternating schedule where you both take equal time off work for the kids.
But my wife won't understand and she will just get upset. I don't want to deal with that.
you should talk to her about scheduling the time for babysitting and come up with a plan. Those kids are yours too so you also should do your part.