Married, Husband Does Not Want Ex Involved

My question involves paternity law for the State of: FL

If the biological father (not proven) wants custody (to spite me) but I am married. my husband & I do not want his involvement in our daughter's life can he still get any kind of custody?

I have a one year old daughter. The one who would be her biological father did not want to know anything about her while I was pregnant, when she was born he denied her and did not want to be anywhere near her. He did not even see her until after her 1st birth day and would get extremely mad when I would ask for him to see her again. I had given up but was just going to leave him alone. If he doesn't want her, we don't want him in her life. Well he had a near death experience was hit by a train, in the hospital he told his family he has a daughter (he thought he was dying). So its been two months since then, where me and my daughter have gone & visited and I've let her stay over 2 weekends and the first time I let her go he brought her back w a bad rash like they didn't change her and this last time I let her stay less time and had given them a specific time to bring her back and he didn't keep to that time so I sat here worried and he reacted rudely every time I called to see where she was & when would she be home. He says that since hes her biological father he will just take me to court and get forced visitation.

Me and my husband love her very much and we don't want to be forced to leave her with someone who will neglect her or just play with her & not care for her as well. We were married after her conception & my husband is on the birth certificate, he has cared for her in every way since she was born and she does have his last name. We were trying to be nice letting him see her while I asked for nothing back but for him to take good care of her when he has her.

Can he really muscle his way in and get any custody even though my husband is right now her father?

Since you were married to your husband when your child was born, Florida may refuse to hear any other claims of paternity.
But, since they do not have a "presumptive paternity" law that I could find, they may also decide to hear it.

If the child in question is only a year old, the court is likely to at least entertain the request for establishing paternity. If they do, and he turns out to be the daddy, the reality is that the court will try to work to make him a part of the child's life UNLESS there is some GLARING reason why this wouldn't be in the child's best interest. You'll be hard pressed to show this, since you have already been allowing him to spend time with the child. You can ask that the visitations be supervised if you feel his skill level or attentiveness to the child are in question, and can ask the court to make parenting classes part of a visitation order, etc. - but courts are VERY reluctant to totally remove a parent from a child's life unless there has been ZERO contact with the child (which there has been in this case). As the child gets older, assuming that the father stays interested, you can expect that he can ask the court to expand visitation to include some level of custody, overnights, holidays, weekends, every other summer, etc.

Obviously, if you want to make the best possible arguement against the court ordering the paternity testing in the first place, you'll want to retain the services of an attorney who specialized in family and paternity law.