I can give you a little insight from the other side (although I’m in a different state). I left my husband last year and withheld our children from him because he was/is a violent drug addict. I wasn’t comfortable with him having access to the kids without a court order in place, as he was a flight risk, was getting further into drugs, and was prone to violence. I filed for divorce as soon as possible and we had a court date approximately 3 months after I left him.
At that first temporary hearing, he was ordered to take a drug test and was given supervised visitation rights. But here’s the important part - I had a shitload of very clear evidence showing that everything I was saying was true. If I hadn’t had proof of a very good reason for denying him access to the kids, the judge would have given shared custody and raked me over the coals, regardless of how long it had been since he had seen them. They may want to reintroduce you guys in a comfortable setting, but courts are very eager to make sure parenting rights are as equally shared as possibly.
In my case, he failed the drug test, but was still able to see the kids every weekend as long as he followed the supervision guidelines. Since then (approximately 18 months between when I left and now), he’s still failing all of his drugs tests, but is also still allowed supervised visitations (although he hasn’t exercised those rights in over 4 months now.) Even further, if he completes rehab, does NA and passes some drugs tests for a period of time, etc, then he’ll be able to get shared custody pretty easily if he seeks it.
Anyhow, my main point here is that even if your ex had valid reasons for keeping the kids away (and it doesn’t sound like she does), the court will still give you visitation rights. But she would have to have damned good proof for her behavior, otherwise she’s shooting herself in the foot because judges do not like the kind of shit she’s pulling. If she has little to no provable reasoning to keep the kids from you, there’s no reason the court wouldn’t give you anything less than 50/50 custody if that’s what you’re seeking. If you were an active participant in their lives before she started hiding them, that’s what the judge will likely base things on.