We hired a reputable company to do our renovations and lived through them with 5 and 7 yo. I had them tested for lead after and both had zero because they did everything required by law. We didn't hire the cheapest dude on the block because this was very important to me. Most of the top folks follow this very seriously. And, you can report them if they don't.

If you have the time (which you don't seem to if both parents work) and if you are comfortable with working with contractors you could go forward with renovations. But, it seems you would be happier paying a little more for a finished house.