I'll advise with the information given.
If you have a choice between June or July, choose June...the earlier, the better. The heat/humidity peaks in July and August. This doesn't mean that it'll be cool in June; just slightly better. Avoid 4th of July, unless you love crowds, and/or have been many times, and don't expect to see everything. (or anything!)
As raptor said, 4 years is pretty far out to be making reservations, but not too early to be thinking (and saving) for your trip.
It sounds as if you want to stay on site. As mentioned, the family ages and composition will make a difference. There are no standard rooms anywhere on site that will sleep more than 5, unless one child is still in a crib. Also, it's possible to get adjoining rooms, but not guaranteed. It's first come, first served. I've gotten them, but was prepared to split up, also.
So the question remains as to how many rooms you'll need, and how will you divide the 18 people to fit into them. Is there some way that one or two of the 7 can go in with someone else? When my daughter's bf came to WDW with us, I put him in a room with my son, and my daughter in with us. Don't forget that guests over 17 count as an extra adult, and how many people do you REALLY want sharing one bathroom?
I usually spend about $1,000 every time I go to WDW...for a weekend. That's for room (around $500 at a deluxe...it varies upon time of year, special rates, level of service) I have my AP, but figure it costs me about $30/day/visit x 3 people = $90 Meals and "refreshments" average $150/day...but we eat at least one sitdown meal at a high end restaurant/day, and have wine, etc with the meal. The rest goes for misc. items.
I'm not the MOST extravagant guest, it can easily be done for much less, but I can't imagine staying on site for less than $200/day for a family of 4 (including admission but excluding travel cost), and it would require lots of planning and scrimping.