I went through a little cr@p with my kid and custody. I found a low-cost attorney through a women's resource center (money was/is not readily available in my little world). It was a great thing to do. I got to see what SKnot's dad could and couldn't do, and got my rights and the custody laws explained to me very clearly. The attorney also had other resouces I could contact.
Document everything, get the papers you have re: his alcoholism and the police involvement, find a lawyer, and get covered.
My custody and child support agreement is open for review every two years, but the restrictions on how things can be changed (and how much) are pretty tight. No major changes allowed for us without very good reason and a full review and more documents, etc. etc.
Your laws may be very different, but if you talk to an attorney you can get a better idea of what can happen.
Is he trying to cow you with the "summers" issue, to get you to accept less child support?
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson