You can petition the court to have the custody order modify based on the reason you have printed here. You should contact a local child custody attorney to help you through this process.
All of Ms. Riley's responses to questions posted on AVVO are intended as general information based upon the facts stated in the question, and are provided for educational purposes of the public, not any specific individual, and her response to the question above is not legal advice and it does not create an attorney-client relationship. Ms. Riley is licensed to practice law in New York. If you would like to obtain specific legal advice about this issue, you must contact an attorney who is licensed to practice law in your state.
Do you have both shared legal and physical custody, or just shared legal with you having primary physical custody? Remember that legal custody deals with the ability of you two to communicate and cooperate over major decisions - I don't see evidence of that inability in all this (yet). If you now have shared physical custody and want to go to sole custody, he may still have visitation, and some of these issues like timely returns and trying to take him on days not his may still exist. His compliance with a visitation issue could be the subject of a contempt, although you could and should seek modification if the schedule is not strictly defined enough. The past bedtime issue is a legal custody decision - each parent decides, but if you feel strongly about it and the amount past your bedtime is excessive for a child of that age, then seek modification to put into place a set bed time. That will be difficult to enforce.
The failure to comply with healthcare and anger management therapy are subjects for a contempt case, not necessarily grounds for a change of custody unless the uncontrolled anger creates a threat to the child's well-being.
You can try to modify depending on what type of custody you have and what you are seeking, if for nothing else to nip his poor parenting choices in the bud. But if your goal is sole custody without any visitation by him, I don't think you can prevail (yet) unless any of these actions creates a threat of harm to the child. Only his anger issues, if uncontrolled and depending how they show themselves, comes close to that.
My advice, go for the modification you seek, but be prepared to compromise on simply getting new and clearer ground rules for visitation/custody time and perhaps that he keep his dating time to when he does not have the child. You may not have enough at this time to change custody. Hammer him with a contempt on the insurance and anger therapy issues.
To questioners from West Virginia & New York: Although I am licensed to practice in your state (in WV, on inactive status as of 9/13), I practice on a day-to-day basis in Massachusetts. I answer questions in your state in areas of the law in which I practice, and in which I feel comfortable trying to offer you assistance based on my knowledge of specific statutes in your state and/or general principles applicable in all states. It is always best, however, to work with attorneys and court personnel in your own area to deal with specific problems and factual situations.
Sign up to receive a 5-part series of useful information and advice about child custody law.