I had a
cold knife cone biopsy last month, jmj. Usually it is outpatient surgery under general anesthesia, and you are discharged after you wake up and can pee. I also went home with percocet (oxycodone) but never needed to take it; I did take ibuprofen for a few days for inflammation and cramps. I also took it pretty easy for the first couple of days.
The difficulty for you with small children is that it is virtually a hard-and-fast rule, from all I have read, not to lift anything over 10 pounds for a month.

I would advise you to adhere to this. You are also advised not to do any
reaching. So it would seem you would need help with the children. Pin your doctor down as to restrictions and when they can safely be lifted.
About 12 days after my
cone I developed rather heavy bleeding. Fortunately this lasted only a few days and went away on its own. I did read that it is not terribly uncommon.
Get good written instructions on everything to expect, and to do, noting all activity restrictions and all circumstances under which to call. The two major dangers are infection or bleeding. These are not common but you should be aware of them. It's a good idea to monitor your temperature during the first few days.
All in all I would rate this surgical procedure as pretty easy -- but I followed the activity restrictions to the letter. (Also, I did get a little constipated, which is typical for me after anaesthesia and the painkiller administered in the hospital, but milk of magnesia took care of that.)
Take care.