Sharon:
I think you'll find that the crowds in the parks are what you'd expect for summer: busy but not overwhelming like the week between Palm Sunday and Easter or Christmas and New Year's. In fact, most American schools are not out by the first week of June, especially in the Northern section of the United States, so crowds tend to be lower at the beginning of June than the end of June, building to the 4th of July holiday.
I'm not a fan of
park hopper tickets for families who are not veterans of the parks or have children. First, moving from one park to the next can easily eat up an hour of your day--and that means an hour to enjoy the parks. Secondly, if you're not a veteran, it may take you time to figure out which form of transportation you want to use to get you from one park to the other. Again, this takes time. Also, having children in tow complicates a move from one park to the other, adding time if they're in a stroller or general crankiness for leaving the parks. Lastly, I strongly feel that you get a lot out of staying in one park for the day, as there's so much to enjoy. Most of all, with the one-park-per-day ticket you save over $60 per person, and I can think of a lot of memorable ways to spend that money at Disney.
Wishing y'all a magical vacation!
Whitney