First... I am not an attorney... I do not work in law or social services, nor am I familiar with Florida laws/courts... just throwing out some things to think about.

1) Have you been documenting exactly when you have the kids and when he has the kids? I used to do this in a little day planner.
2) Have you been documenting expenses that you have paid... keeping up with receipts/paperwork? Do you have proof that you have presented the expenses to him and asked for reimbursement? I would have something in writing there... e-mails requesting reimbursement with copies of the receipts, etc attached. Or if e-mails are not admissable as evidence... then send it certified mail. Something showing that you have made him aware of the expenses and have asked for reimbursement.
3) As far as I have read... he is allowed to have a competent adult pick up / drop off the kids and watch them. You do not have to meet that adult. (Though I understand the desire to do so.) It's no different than if he was dropping the kids off at a daycare... he does not have to get your okay on which daycare he chooses... if that makes sense. Having a DCF investigation really doesn't mean anything. Anyone can have a complaint made against them and a case opened. Charges would mean something. Now... if the kids are being abused... have you documented that with photos, doctor's statements, etc? Did the DCF folks "find" anything of concern? If so, they will have that documented. Leaving the kids unsupervised... you said it's not against the law. I don't think it matters if you like it or not. (Not being snarky... just playing devil's advocate.)

Personally... (as I stated, I have no professional knowledge in this area) I think the only real thing you have is if he is not getting the kids when he is supposed to. Document that. Not sure if a judge will give you full custody... may end up just getting onto him and "scare" him into getting the kids when he is supposed to. Which then means the kids would be staying more with the girlfriend you don't like. But... the judge could side in your favor. Just another perspective and some things to consider. Good luck.