The only real question you seem to have asked here is, "Does he have a chance?" He does have the right to make the request, and he could in theory win. It seems unlikely from the facts you describe, but it's hard to say more. Unfortunately, it is often quite meaningless to guess chances on the outcome of a court proceeding. There are two reasons for this.
First, we don't know enough about the case. All we know is what you've written here - which isn't much detail - and presumably, the other person involved would give a very different version of events than you would. A judge hearing a case hears both sides, and tries to give equal weight to both. The less information one has about a case, the harder it is to predict what will happen - and all we know here is what you've written.
Second - single-event probabilities are arguably logically meaningless. Consider this: Suppose I said you have a 75% chance of winning the case. Would you feel reassured? And, suppose I said that, and you lost. Would I have been wrong? Probabilities are meaningful only when you are considering a lot of similar events - but legal cases are all so different that it's hard to draw valid comparisons.
The general rules involved are these: Under Oregon law, decisions about legal and physical custody are made according to the best interests of the children. Obviously that's quite vague, but the law sets forth a few standards for determining the best interests of the children.
The most commonly followed guiding principle is that a child should remain with the parent who spent most time with them before -- the "primary custodial parent." It sounds like this is you, so you have that advantage. The law also presumes that it is in the best interests of the children to have an ongoing relationship and continuing contact with both of their parents. If the court must decide which parent is awarded primary legal and physical custody, it is more likely to grant it to the parent who has shown that they will encourage an ongoing relationship between the children and the other parent.
In a relocation case, the parent moving generally has to show that the move away from the other parent is in the best interests of the children - not merely in the best interests of the parent. So you may have a hurdle there. But as the primary custodial parent, the odds are still on your side. Most likely you'll end up with some sort of compromise - that's what usually happens in custody cases.
To best increase your chances in a court case, you should consult in private with an attorney in your area. I realize that isn't the most helpful advice, but I do believe it's the best.
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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.