First of all, what time of year?
December to April is high season and is FAR more expensive. Also best chance of good weather. Although weather is increasingly unpredictable all yr round. Christmas/NY is peak peak peak.
May to November is hit and miss weather wise (May is worst) and not too bad price wise although summer (Jul/Aug) is getting pricier. But still cheaper than peak.
3 kids - tbh you may find it tricky to find places that have big enough rooms. Are you happy for one of them to be in with you?
Always check prices on the resort’s own site as well as booking.com etc. Sometimes they have better offers especially if you sign up to their site.
Sometimes you can get a good deal if you book somewhwere that isn’t open yet - but you are taking a punt on it opening on time.
I would suggest looking at: Centara Grand, Hideaway, Kuramathi, Lux, Bandos, Reethi Beach, Adaaran Select Meedhupparu, the various Sun Siyam resorts as mentioned above. All of these are on the more affordable end and have family rooms. All but Reethi have kids clubs.
Not everywhere has a house reef around the island so decide whether this is crucial (ie do you want good snorkelling right off the beach). Of my list, Lux doesn’t have a reef and not all of the Siyam ones do.
Be aware that Kids Clubs are generally aimed at little ones ie gentle craft rather than watersports.