The mother knows he did this. What caused them to break up was one night their house was broken into by a criminal he had been working to put away and Gracie's (the MC) room was destroyed by the character. This scared the mother, and this is why she told him to stay away
Here's the "not believable" part, IMO. I can understand if it breaks up the family initially. That sort of maternal panic really does happen. But if she sees him putting away the criminals in the press, eventually she's going to realize she overreacted. I really do think you need to beef up the continual nature of the problem. Every type of psychic power has a downfall. Here are a few scenarios that would both make it more believable and that have worked in other series:
1. The psychic is a "touch psychic". Bring the person an item and they relive the event until the person's death--including emotions, actions and fear. It's an ugly sort of psychic talent. The person really doesn't WANT to help, but because they're so tied to each person, they can't NOT continue to help until the criminal is caught.
2. The psychic hears the voices of those who just died, or are about to die. The psychic seldom gets the opportunity to say NO. They're badgered by the recently dead until they help.
3. The psychic is a "premonition" psychic, picking up on flashes of events yet ot happen that can come any time of the day or night. This kind of psychic wouldn't necessarily work with the police except to warn them of something they DIDN'T already know about.
A touch psychic would insulate his family and he probably would refuse to help the police if it would be a danger to them. The psychic who is the "I see dead people" sort can't help being involved, but the family would seldom know about it, so it's not something that would break up the family--and the event with the criminal breaking in probably wouldn't happen.
The premonition psychic would likely never encounter the killer. If he got a sympathetic police chief/sergeant, etc., his involvement would never make the press.
So, I think the believability issue stems from two problems:
A. The Dad has a relationship with the police that puts himself and his family in danger. The type of psychic he is has to be carefully created to make that believable (since psychics working with the police are often on the fringes of believablity anyway.)
B. The threat to the family has to be REAL and CONSTANT enough to warrant the family breaking up. The Dad has to be unwilling to fix the problem AND the Mother has to not have regrets. If it's the only problem they had, it's stretching believability. I think you might need to do a "straw that broke the camel's back" sort of relationship instead. There were already other problems--maybe he drank too much to keep the psychic stuff tamped down? He's sober now, but Mom knows (not the MC, but MOM) that he could go off the deep end again any time. That's not something you discuss with your teenage daughter. Or maybe they only married because she was pregnant. He was exciting, but in day-to-day stuff they didn't really mesh. Etc., etc. Unless part of the book's plot is to get them back together, you just have to make the break-up and continued lack of contact enough that the reader will let it slide. So far, from what I've read, it's not.
Just a few ideas. Good luck with it!