Marie,, please hold off on buying Museum passes, seems alot of people tout them here,, but they are not always nessesary,, and in fact, with your list, rather needless buy.
Most of my trips to Paris ARE in August, and lines are not much worse then other times( I sometimes wonder if all the posters go tell people about how bad it is in August, have in fact been there in August!), in fact, they sound better then the ones in June or Sept.
Second, you have only named two places you are committed to visiting that you would even accept the MP, the Louvre and Versailles, and at the Louvre it is completely unnessary. I have never used one there, I have gone for numerous visits, all in July or August. There is a lesser known entrance, with ticket machines to purchase ticket from, and the teens under 18 are free also.
A pre purchased ticket DOES make good sense for Versailles, ( kids are free there also) and can be purchased from their website in advance.
Your apartment stay sounds like a great idea for money saving, just having snacks on hand to keep teens fed will save you money.
My teen boys loved seeing the Catacombs,, check out website.
My kids also enjoyed the HOHO buses, especially when we went aroud the Arc D'Triomphe traffic circle. BTW, the Arc has great views , and we never have enountered overly long lines to go up it,, a good alternative to going up the ET,, which always seems to have long lines, ( and the MP does not work for ET anyways) . You can also save money if you decide to go up ET, by using stairs, they aren't that hard. Going to top is not ness for good view, view from 2nd level is great.
I will offer one warning though, the Musee D'Orsay, which is a great place to visit ,, often has long lines, we lucked out last summer with only a 15 minute wait,, but I beleive that is an exception, so , that site is one that the MP would be very handly to have ,, also the Orangerie,, . It depends if you actually want to go to these places.