Can my ex-husband stop me from moving in with my boyfriend of 2 years?

Generally speaking, your ex-husband cannot stop you from moving on and finding a new life with a new husband.  Remarriage rarely constitutes grounds for taking custody away from a custodial parent.

However, there are a couple of things that you should keep in mind.  If you just move in with your boyfriend before you are married, some judges will frown on this.  In the modern era, it's less of an issue than it used to be--- but some judges will place morality clauses into orders which prohibit any overnight guests of the opposite sex while the child is in that parent's care.  This means that, potentially, your ex-husband could take you back to court and ask the court to place this restriction on you. 

The second factor turns on any issues with your boyfriend/fiancee.  If he's a nice guy that is really stepping up to help you raise the child, then you shouldn't have any problems if you ex-husband tries to take you back to court after remarriage.  On the flip side, if your fiancee has some type of history that poses a risk to the children, then this will give your ex-husband a basis for seeking full custody if you remarry.  Issues can include him having a history of violence, he's a registered sex offender, he has a drug problem, or he neglects the child when you leave the child in his care. 

These are the two areas where your ex-husband could possibly cause you grief in a modification hearing.  Otherwise, he cannot prevent you from remarrying and moving on.

Under the laws of all states in this country your "ex" cannot preclude you from moving in with your boyfriend. You have the right to reside with whomever. He could make issues with respect to custody of your child due to your living arrangements but such does not impact upon whether or not you are a fit parent. I suggest that you consult further with a family law attorney with respect to this matter.