WH - I would not be penny-wise and pound-foolish on this - get a lawyer.
I suspect a judge would want to know how your living expenses have changed since moving in with the boyfriend. For instance, do you pay him rent? If so, how much and how does it compare to your previous rent? Utilities?
Really, it seems that these are the only expenses that would be different since moving in with him. If you're not paying rent, then the courts might decide that your expenses are that much lower and might possibly decide that your alimony could be reduced by that much. But I would imagine that this varies a lot by state and only a lawyer could help you know how best to attack this.
I DO think that this is an opportunity to have child support recalculated based on his current income. That counter-punch might also cause him to reconsider the whole fight. But again, I think you really need to consult an attorney to find out how best to proceed.