Rubberbands
These people sound like they have serious problems. This isn’t the kind of thing you can solve with a phone call. They are ignoring you because they have issues. Don’t blame yourself or your side of the family. Some people are difficult to deal with and get along with. Its very hard for them to change. If they want to be left alone, leave them alone. However if there’s a chance to have a good relationship with the kids (your cousins) then go ahead and figure a way to pursue that. But the parents seem like a lost case. Not that they can’t change but people who are this way and have so ingrained this behavior will have a nearly impossible time of changing and undoing what they did.
Recognize that you can’t change people. You can’t tso stop trying. If they want to change they have to make up their minds that they want to change. Until that time, the situation will not improve. You will only be making yourself crazy and stressing yourself over something you can’t do anything about. Leave them be.