I needed a condo for two nights before a cruise out of Port Canaveral next February and last night booked a fully refundable three bedroom / three bath condo here: Diamond Resort Grand Beach Phase 1. Take a look here at what the condos and resort looks like plus amenities offered. Website:
https://www.diamondresortsandhotels.com/Resorts/Grand-Beach?mkc=GOOGLEUS
This ran me somewhere with taxes and resort fee around $330 - $340 a night, so under your $400 per night budget. This can be booked directly on their website or on booking.com, expedia, etc. I booked direct. There are two king beds, two twin beds, and a sofa sleeper, so each of your kids could get their own bed (a twin for each of your sons (would share a bedroom), a king suite for your daughter, and a king suite for you) leaving the common area for late and early risers, as well as the balcony or patio.
They offer a better rate that is not refundable, but I didn't want that as I am not totally certain that someone in our party might do a timeshare trade the full week before or something like that and want things flexible for now.
There are sites like TUG2.net and Redweek.com have good full week Fri-Fri, Sat-Sat, Sun-Sun owner timeshare rentals with no made service at better prices than retail for sure (good option if you are doing a full week and don't mind not having daily maid service), but we just wanted two nights.
You could book this fully refundable (could be a default) and then look for something you might like better or something that is similar, but better priced. This particular resort has very good reviews.