Hi S.,
I noticed that no one responded to you with a Catholic church suggestion. I am Catholic, my son is baptized Catholic and my husband is Lutheran. We are registered at St. Mark's in Southwest Ranches (next door to Flamingo Road Church - Flamingo Road just north of Stirling) and I know that they have a "babysitting service" for ages 1 to 4 1/2 during the 9:30 mass. The kids basicallly do some biblical stories and as they get older some arts/crafts activities. Website: http://www.stmarknet.com/masses_%26_services.htm
We also attend St. David's in Davie (just north of Griffin on University Drive) and they are super family friendly but the expectation is that children will attend mass with you. The 10am mass is geared for that and it rarely lasts longer than 40 minutes. Very traditional mass but the priests understand that little ones have a short attention span. They always have good music, understanding that is often the favorite part of the kids. Website: http://www.saintdavid.org/church.asp. My non-Catholic husband is very comfortable at St. Davids which is part of the reason that we attend frequently.
I'm guessing that your parish is probably Our Lady Queen of Martyrs. It is a very Hispanic church next door to St. Thomas High School and has always been super child friendly since they also have a Catholic K-8 school there. They aren't online, so you would have to call them.
You can find some info on parishes and contact info for them online at: http://www.miamiarch.org/
I hope you can find something that meets all of your needs and makes you feel welcome. I also attend the St. Gregory Mommy and Me group, since St. Mark's suggested it when I asked for such a ministry. It is great, you can read about it on their bulletin at: http://www.cherubim.org/
God Bless, C.