Shut up and mind y'own bidness. You can pray for the preacher, the mother, and the child, but beyond that, leave it alone.
I read a story about a letter David Wilkerson recieved from a teenager. It seems she found out that her best friend was sneaking out of her parent's house nights to run aroundg with one of the rottenest boys in town. She told her friend she knew, and tried to talk her out of seeing the guy. Her friend refused, and said she didn't care what she thought, she was gonna do what she wanted. THe teenager asked Wilkerson if he thought she should tell on her friend, and he replied nope, it ain't up to you to convict her of her sins. The Bible says "You sin will find you out". Eventually, the girl would repent or get caught. In either case, it was up to God to deal with the girl, not her. He isn't asleep, nor has His arm gotten any shorter.
I agree with Gerald that a preacher who refuses to support his children, in or out of his house, shouldn't be in the ministry. He might deserve the other things Brother Creasey specified, maybe worse. But before we limber up the bullwhip, let's rememeber we don't know all that's going on there. It wouldn't be the first time I ever heard of a woman refusing to allow an illegitimate father to give her anything, and/or disallowing any participation from him in raising/supporting the child. For all we know from what you wrote, that might be the case here. At least nothing I read would put it out of consideration.
Certainly, if she wanted to she could take him to the cleaners by way of the courthouse. The courts have it in for deadbeat dads these days, and he wouldn't have a leg to stand on if she she took him to court. One blood test and he's on a court-monitored and enforced payment schedule till the child's emancipated. If she isn't doing that, maybe she doesn't want to, for whatever reason, and that's her decision, not yours. Or Gerald's.
There are a lot of scenarios that could be playing out, and all you can do is speculate about what's happening unless and until your friend decides to inform you further. If you couldn't sit through a service with him preaching, don't go to hear him preach, not until after God convicts
you, and you repent of your unforgiveness towards him. So get off your brother's back and mind y'own bidness, at least until God tells you otherwise.