If you are doing a 7 month renovation it's obviously pretty major. Can you take the kids to family during the day? It's not up to the contractor to be looking out for kids playing where they shouldn't and that puts a lot of stress on you.

Move out. The work will go faster withou you under foot.

Ok,
Use air scrubbers from start to a week after completion for air quality.
Keep plenty of shoe covers for contractors as they have been to places you simply do not want in your home.
Make sure you get picture updates from the contractor and speak with his workers to build a relationship as 7 months is a lifetime.
Buy coffee( brew really good coffee) as a token.
Make sure all debris is removed as quickly as possible and let your neighbors know if they see anything strange to alert you.
Hope this helps

Thanks everyone! For the most part the construction will not be in our main living space, just new construction and conversion of a garage into a family room. The contractor has planned to put up a temporary locking door to keep my kids away from that part of the house, and thankfully I have a portion of my yard that I can contain them in as well. We have contingency plans to get out of dodge if we have to. We have a separate AC unit for our main living area that I'm hoping won't be too affected by the construction dust. Should I get portable air filters too?

Yes
Air scrubbers for any dust and duct them to outside