Were you looking to rent the entire pavillion or just the outdoor area (labelled south side patio is what you would want when asking) The outdoor area is a tad more reasonable, covered, has picnic tables and sounds like is all you need, plus it has a bbq. Cost is $155(ish) as long as you do not rent it on a fri/sat/sun. If you do, then you have to rent the entire pavillion and then that gets $$$$$$ So, if you can plan for the get together to be M-Thurs, I think this is a great place and $155 split between a few families will hopefully make it more feasible as this is really the best place for what you are describing. Kids can run around, there is vb courts, soccer fields, tennis courts plus Breck elementary 200 yards away and can walk over and play on the playground equipment.
There are not many public parks around Breck due (guessing) to 1) fairly small town 2) high cost of real estate 3) tons of forest service/open space around making protected open space not as much a high priority as it might be in a large urban town ala Denver/Houston 4) longer winters. Unfortunately, that does not help you.
Maybe Kingdom Park if there is not much going on, believe they have BBQ's over by the softball field. If fields not being used, adults and kids could play a game of softball/kickball...have a few picnic tabels. Inquire with town or Rec Center if you call and ask about outdoor pavillion only rental.
Another option might be to see about renting a room at the Breck Rec Center for the meal portion (yes, indoors so not as exciting) and then getting a 25 punch pass so majority of adults/kids can go inside and play basketball, raquetball, swim...
Final thought would be to see about holding the get together at one of the complexes you are staying at. A few might have an outdoor bbq, seating could be hard for that many.
Or try Frisco and Walter Byron Park (I would recommend reserving). If cost is anywhere close, I think Carter is better option though.
Best of luck.