Kim, I have taken my 11 yr old and 13 yr.. on separate trips.
There is no time the line in summer for ET will be short.. but your kids are the perfect age to take the STAIRS.
You can try and prebuy tickets.. and hopefully you are lucky.. but there are so few available for each time slot that they sell out in minutes after they become available.
The stairs are cheaper, and even when the one set of the elevators broke two years ago.. and the line for tickets for the remaining functioning one was 3 hours long, the line for stairs was 30 minutes..
My son enjoyed the stairs.. he would run ahead of me and double back to goad ( cheer) me on.. but I made it.. and I am not a super fit person!
I will be blunt, ,renting an apartment for 3 days is not worth the hassle. Apartments must be carefully reviewed. You must pay attention to check in and check out times.. you cannot store luggage at them like at a hotel if you have a late flight or early arrival.
I have rented in Paris and had great experiences.. but always for the week minimum.. I just wouldn't do it for a few days.
Another consideration.. most apartments ,, except expensive ones.. do not have ac. In August.. you may or may not need it.. but , if you need it,, it will be crucial. Air does not move in Paris .. the stone buildings and pavement make it suffocating when its hot.. and most public buildings and museums have very poor ac.. you will barely feel it.. so , after a hot day on your feet all day long.. a cool retreat is not to be under estimated.
For first timers I still recommend the 4th, 5th and 6th arrondissmonts .They are central to many sites and most folks enjoy the old Paris feel ( narrower streets etc).
Citadines is an Aparthotel.. the one is St Germain is well reviewed, and I know the location.. perfect.. but , its not cheap. However with a small kitchenette you can save some money feeding boys just by having snacks and juice in unit.
PS Highly recommend you take kids to the Invalids Army Musuem.. never crowded,, kids free, and it runs from suits of armor , battle axes and muskets, to WWII and tanks.. my kids loved it.. a nice change from "art" museums.