If budget is a primary concern, then I would suggest Amerisuites on 17th in Ft. Lauderdale. You can get parents and kids into one suite and it includes breakfast and is not as expensive as Embassey Suites right across the street.
On our last stay at the Amerisuites, we took a taxi to Miami to pick up a cruise for $80. That is only $20 per person (there were four of us) and I believe that was the most economical way to do it; not to mention being the most painless way. If I remember, you have a bunch of kids with you. I would certainly not rule out this option.