Mom hangs in New England all winter and then summers in Florida? Complete opposite from what most do around here! Love it.
Most kids around here get out of school mid/end of June. The week after fathers day is usually a great week because most of the activities start daily operations (instead of weekend) and a lot of the kids are still in school. If you are thinking early June...yes, you should definitely check out activity schedules before you commit to anything.
We have done Smuggs in the summer twice.
The first week (mid June) was a bust, mainly due to weather and there isn't a heck of a lot to do "indoors" in the general area. The second time (mid July) the weather was perfect and we did resort activities, nearby horseback riding and zip-lining.
Just my opinion, but I consider Smuggs more of a "resort" vacation.
If your looking to explore the area, be prepared for a bit of a drive. Here is a link from their site:
http://www.smuggs.com/pages/summer/activities/area_attractions.php
There is a big hot air balloon festival mid June on VT/NH line:
https://www.quecheeballoonfestival.com/
Personally, I adore the White Mountain region of NH and I still prefer it over VT anytime of year. I simply find more to do with less of a drive. With that said - I would suggest if you have been to Lincoln already....then I would try the other side. RCI is best for this area and I would suggest either Eastern Slope Inn or the Suites at Eastern Slope if you want to be in the middle of restaurants, shops, etc. Personally, I prefer Bartlett because it is NOT in the middle of all that. The Suites at Attitash Mountain Village or River Run
Another great option which I think would a good mix for adults and kids is Newport, RI. I would suggest any of the Wyndam properties with Long Wharf being on top and the Wellington.