"I have thought about things and the one thing that kind of scares me the most is that when I left on Dec 16th, 2011, I let him have our daughter for 3 days (2 overnights) on New years."
So he was OKAY to watch her when you NEEDED him to, huh?
"After that date, we got into an arguement about him telling me to stop travelling around Florida and get a job and refusing to pay things for me if I do not."
Sounds less like an "arguement" and more like a, "He told you to start acting like an ADULT and be a PARENT."
"I told him I cannot wait to see just how much he is he going to have to pay me by the judge and also that our daughter's last name will be changed to mine."
First off, you will get NOTHING for alimony, and second, NO, they will NOT change your daughters last name unless there are EXTREME circumstances, of which you have none.
"He was irrate and called me a demeaning name. Since then, that is when I have refused to allow him to have her overnight and at his house with only supervised visits from me. Should I be worried?"
Nope, not at all, PLEASE let the judge know that you have denied him parenting time because he called you a NAME in the middle of an ARGUEMENT, where you were demanding that he give you MONEY and pay your BILLS. PLEASE tell the judge that, your daughter DESERVES to be out of your care.
"The main reason I keep telling him why he cannot have her outside of my stipulations is because he does not have the bond she and I have, that he is essentially a stranger to her and not familiar with her. I guess I should have not allowed her to go over there on New Years for those 3 days."
Actually, "letting" (I put it in quotes, because you didn't LET him do anything, as the child is not YOURS to do with as you please) her spend the three days with him was about the ONLY thing you did RIGHT.
Why give a "senior" discount, they have had plenty of time to raise the money...