First of all, if he has not been consistent in her life the visits need to start off slow at that age.. during the week after school 2x's a week, no over nights until he completes the consistent after school thing. If you can, invite him over for dinner at your house so that you can see them interact together. He will not know that it is a supervised visit, they do not react well to control, usually. She will see that you both get along and will phase into their alone visits better. If this is not acceptable to you for your reasons then you can even meet at McDonalds playland and do the same. A child that age should not be thown into over nights until you see that they are comfortable with that. If she is just getting to know him again this will work out best for everyone. He may not agree with this and if so and you are the custodial parent. Too bad for him...it is her feelings that matter not yours or his. I would set a 2 month date on the after school for 2-3 hours after you do the supervised visits...it is best not to use that word. Just set the visits up that way. If you do not get along you do not have to sit at the same table. Bring your laptop or borrow one that can keep you busy so that you are not leering at them. Encourage your daughter that this is your time with daddy. Mommy is busy but I am here if there is an emergency, she will need you for potty breaks. When you go for potty breaks be posative..example; Isn't it great to ssee daddy. Are you having fun? Parks or Chucky cheese is a great place for visits too. She will be stamped with a number that only matches yours and he cannot leave with her.
After the 2 months set up alone visits where he has to come pick her up and drop her off after 2 hours with a booster seat of his own. That is the law...You do not have to provide one for him if he does not have it you can deny a viit until he does. He can get one at a garage sale or good will if he soes not have much money, there is not excuse for ignoring her safety. What else will they ignore?? These kinds of visits are so he has to find something to do that focuses on her and if he does bring a girlfriend, so be it. It is his time and if she is important to him that gives your daugher a chance to get to know her slowly as well. If you do not want a man in your life that is fine but trying to control his life will build resentment instead of respect. It will also let you see his significant other interact with her. The courts usually need a reason to deny him bringing her with. It also shows no jealousy and that you are over him by respecting his right to a social life. If she is abusive or argumentative then the stipulation regarding no cohabitation can be submitted. If it interferes with the best intrest of the child.
After your specified time that you set for this type of visit and he is following through on all the visits you put the stipulation in for over night and the weekly after schools. I do not know the reason for her being in special education? My son was too. He had an emotional impairment with anger issues. Her handicap cannot be ignored so if it takes longer to be ready for an in crease in time that is fine but don't let her manipulate you either. If she has autism then there is much for daddy to learn. I started with one over night and the 2 days a week after school. If you want to increase the after schools to be flexible and he returns her on time that is always good too and he is showing respect and responsability and you can feel safe giving him extra time with the beautiful child you both created.
With those who are not consistent they either follow through or hang themselves by making excuses why they cant come or do not show up or drop off on time. They end up in contempt of the order and go away again. Let them know this will show your daugther how much she means to you. I hope this is helpfull to you and these are just examples of what worked for me. Most of the time they cannot handle the extra responsability and go away as I said before. Time will tell. I was a child advocate for many years and I also have 3 children that are involved with visitation orders. They have to be modified to what the child needs not the parent.
I also agree regarding the visitation order being in place and on file with the school. Her teacher and the office should both have one. I hope for her sake that he brings smiles to your face by being a great dad and saying...what ever it takes to make her feel safe and happy. I hope this gives you usefull suggestions that you can modify to fit your family.
I wish you all the best.