He just tells her if she moves she can only have the kids on Sat. and Sun.
This is not entirely accurate, surely a lot of his bluster is his sense of Entitlement and Control. I don't think he can unilaterally change a parenting schedule. If he has Decision Making, does that mean he is also Residential Parent? It's possible that he may be able to insist the children not change schools - if he resides in their school district. Both DM & RP ought to be assigned to her due to the actual parenting percentages but it will take a court to make changes to reflect the current reality.
In general, no matter what, it's a good idea to document everything. Like father not visiting his son in the hospital, the number of times he does not visit during his custodial schedule, or any instances where he blocks decision-making.
Yes, documentation is crucial. When courts hear phrases such as "he always... ." or "she always... ." they're likely to view it as non-specific "he-said, she-said" and hence not very actionable. But with the specifics and supporting documentation it can become actionable. Be aware that incidents older than about 6 months or so can be considered "stale" and ignored except at part of a pattern.
Also, the courts pay more attention to the parenting behaviors (his behaviors with the children or that would affect the children) than the adult behaviors (his actions with you and others). In other words, he could be a poor example of humanity but the court will focus on how it impacts his parenting or parental contact.
What is the current written parenting schedule? Is it equal parenting time or does one of the parents have majority time - on paper?
It sounds like a time for seeking more parental authority, often begun by filing for
Change of Circumstances based in his minimal parental involvement, Lack of child support may also be a factor but if he's not currently ordered to pay or reimburse then any change would just be going forward.
A big factor in D's favor is that he is unwilling to share, though it may be hard to prove that with just a simple claim. I recall when I had my Custody Evaluation in 2007 the CE, a child psychologist who was well respected by the court, was very perceptive and wrote "Mother cannot
share 'her' child but Father can... .Mother should immediately lose her temporary custody... .If parents attempt Shared Parenting but if it fails then Father should get custody." Yes, court just proceeded to the next step in my divorce process, but it set the pattern for what came later, I went from "on the outside looking in" to a parent who should be involved.
If your D already has official majority time then she can file seeking Decision Making and support it with his documented minimal involvement and even obstruction.
Generally there are no quick fixes but if D gets documentation of his behaviors that he may not want exposed in court then he may prefer to stay in the background and let the changes happen. But the full Decision Making does need to change or else this problem will come up again in the years to come. That's where well thought out boundaries come in. Figure out what firm boundaries are needed henceforth, how to get them and how to defend them long term.