The reason there are no family bedrooms between Boston/New York/D.C. and Florida is because only Superliner (the double-deck passenger cars) sleepers have family bedrooms, and these cars cannot be operated in the Northeast (primarily clearance issues due to the height of the cars). The only Family bedrooms on this route would be those on Auto-Train, which does not go north of D.C.. You could drive to Virginia and carch the Auto-Train from there if you are looking for cheaper fares, though by the time you allow for the cost of hauling your car (and the drive to VA), it might not really save anything. Also, two adults and three kids would really be tight in the family bedroom.
The sleepers on the Florida trains (except the Sunset Limited, which originates in Los Angeles) all use Viewliner sleepers. These have two deluxe, one special (mobility-impaired), and 12 standard bedrooms. The two deluxe rooms can be combined into one "suite" (this is apparently the rate you were quoted), but it'x very expensive since you are really paying for two rooms. Also, book early, because there are only four such rooms (2 potential suites) on each train (and the prices only rise as the lower-priced tickets sell out anyway). Two deluxe rooms are no doubt the most comfortable (even luxurious) accomodations for your party size. One deluxe room would basically be unworkable for two adults and three kids (two standard rooms would give you four adult-size bunks, but would require splitting up your party). If cost is still an issue, just take five coach seats. These are far more comfortable than airline or commuter coach (really, there's little comparison).
The Florida trains all originate in NY, so you may as well change trains there. There is really no need to travel from Boston to NY by reserved/business class, or on Acela Express - they just cost more. If you go coach all the way, NY is a particularly good place to board for the best choice of seats.
Interestingly, there were plans to extend one of the two Orlando trains north from NY to Boston, either via Providence or Springfield, depending on which rumor you heard last. You could then travel to Orlando without changing trains, but nothing has been heard of these plans for months. Also, there were sleepers (viewliners) between Boston and D.C. until quite recently, but they were removed due to a shortage of Viewliiner sleepers needed for other trains. Presumably these sleepers will return eventually, but again, exactly when (or if) depends on who you ask.
