The first question is how your move will affect his parenting time. If the kids are younger than school age, the move might not affect his parenting time at all. You say ten days, so I'm guessing Fri-Sun?
And maybe another overnight somewhere? Again, with a "short distance move" (less than 60 miles),
the impact on his parenting time may be minimal. He is probably saying the move isn't in the best interests of the kids because it negatively affects his parenting time with them, but like I've said, if the impact is minimal, that may not be a winning argument for him, especially if you had to move away for financial reasons.
We would need more information about what kind of a dad he is, what the nature of his relationships are with the kids, and more information about where you are moving and why. The bottom line for a judge is whether or not the move is in the kids' best interests.
Its very unlikely he would get a change of custody, based on a short distance move, because he'd have to show the move was a "substantial change of circumstances"- and I don't know based on the facts you've provided he could show that. Worst case scenario in these kinds of cases, usually, is you keep custody and move back. However, your situation seems to call out for some sort of compromise where the parenting plan is modified to accommodate the distance, and give him some extra time, if need be, around 3 day weekends, holidays etc.
Bottom line is to answer your question we'd definitely need a lot more information and detail.
Barring evidence something is going on at your home that endangers her health or safety, it is in the best interests of a 9 yr old to visit you. Did her decision to not want to visit you come out of the blue or did something happen during a last visit that caused her to react this way? You never know with young kids. But assuming nothing has changed, you are probably right that your ex is somehow managing this, which is wrong. I would continue on with the current plan, and hopefully get all your make up time, use it to keep the bond with your daughter strong.See question