First - (after get real legal advice) is stop allowing back and forth communication through your daughter, kids shouldn't be involved in legal drama.
Second - If it's not in writing it never happened so phone calls aren't much better. It's too easy to claim confusion over what was said and how could you prove what was said anyway? He'll just call you a liar later on. If he calls ask him to write whatever it is he is offering on paper and mail it to you. You're obviously not comfortable with taking him at his word nor has he given you any reason to think he is trustworthy.
Third - You decided to proceed on taking action to get what is owed you. DO NOT stop that process until AFTER you receive the money you are owed (or an amount you are willing to accept). You will complicate your case if you file and then cancel motions and you might even cost yourself what you are owed.
You filed, the clock is ticking, he needs to pay you before time runs out or your motion will be heard and a final ruling entered. Be fair but firm, he's in hot water, not you. If you agree on an amount and he pays it in full then you can call off your motion, not before, the clock is ticking on him.

