If he didn't marry or have a child with her he could have just moved out and let the lawyers deal with it.

He did have a child with her however and that carries legal and financial responsibilities but they too should be dealt with via the courts.

While he was still married he employed her and then entered into a relationship with her which went sour later.

Gibson still comes out of this worse.

If someone is trying to extort money out of you illegally let the lawyers sort it out and cut all ties with the person.

Violence + a child + plus sexist, racist rants on tape = Almost Worst Case Scenario (if he had murdered her as well he would have got the full set).

Gibson can afford the best common sense money can buy (advice) he should buy some of that and lay off the booze a bit more.