The trouble is that people who breed this kind of cross are not interested in the dogs they use for the breeding just the money they can ask. But it would be better to forget the cross and just try to deal with the problem, as biting is involved I would suggest you try and find a
APDT trainer who will come to your home and look at the problem. With situations as worring as yours it is best not to offer help on line as it is not possible understand without seeing.
If children were not involved you may be able to avoid the situation where he is getting upset, but with children you can't take the risk.