If you get a Suite you likely won’t need a 2nd room for the kids as they usually have 2 rooms.
Not all Hyatt Properties have suites (Hyatt Place & Hyatt House do not), but a majority do.
They cannot be combined with Club Access Awards (though a fair amount of suites at properties do confer club access).
Maybe off topic, but if you get to 60 nights (through another 10 nights stayed, Money spent on World ofHyatt CC or a combination of both) by 12/31 you’ll also earn:
(2) More Suite Upgrades
A Category 1-7 Free Night Certificate (I would say a $1,000 Value)
Globalist Status until February 2021 (Very Valuable if you’re staying that many nights a year especially with kids) Biggest benefit for families is automatic Club Access or Complimentary Breakfast (meal or Buffet) for 2 Adults and 2 Kids.