Unfortunately a lot of men falter without the power behind the throne. First of all I am very sorry for your situation and getting through it will not be easy, but you sound like a very level headed intelligent woman and I am sure you will do the right thing(s).
Have you gotten a legal separation yet? I would establish that order of business as soon as possible if not, because a notarized agreement isn't going to hold up in court as well. That will establish everything in the arrangement by order of the court until the divorce can be finalized and then keep a journal of all the incidents of no child support and failures to comply with the separation agreement. This will get you everywhere in court.
You are doing the right thing and as long as you are doing what you feel is right and searching for outside input to help keep things in perspective. Also make sure you have a supportive person in your life that will let you vent, you need someone who will realize that just being able to rant and rave about something even if you can't change it can be a healthy release.
As far as worrying about your child that can be a bit more complicated depending on your beliefs. I have a tendency to be a bit of an anxiety prone individual myself, and I had to learn a way to cope with my inevitable thoughts of doom about virtually every situation known to man involving the care of my children even with very responsible and capable people such as my husband and my mother. My husband and I have a very strong belief system and now that I am more secure after much practice in my beliefs, I am able to get through those difficult moments. We believe that everything happens for a reason, and as far as tragedies are concerned, when it is your time it is your time and it is all predetermined. A person can give themselves a whole list of medical problems along with anxiety when it comes to considering the endless "what ifs". I believe that if I am living my life the way that god instructs (with obvious recognition of the fact that we are all sinners and quite imperfect or we wouldn't need God's help or blessings) and I ask for his forgiveness daily and protection and guidance then I have done all that I can do and it is absolutely out of my hands. This doesn't always instantly comfort a person, however if you truly believe it, it can help a great deal.
My advice on the legal part comes from being that supportive person for some of my friends and family and having a 13 year old son who has an alcoholic father who is 40 and recently sober for almost a year for the first time. I have given quite a long list of requirements and conditions for involvement with my son as well with regards to his physical and mental health. Mothers are supposed to protect their children. The best advice about being able to rely on him is don't or his family. It can be really though, but learning how to manage without any help at all will help way more and then if you actually do get some help then it will be a pleasant surprise.
Good luck and I hope if nothing else this gives you some possibilities to consider for your own situation.