It depends on the extent of the irreverences in that parish, I don't know the concrete situation. If the irreverences, heresies, or ambiguities in doctrine are dangerous, which the priest is preaching, then it's better not to go there. In this case, in the example that you gave, it is justified to just be at home just like what we did during the Soviet period when we had no place.
The father of the family has to organize at least once a month a real trip to another place to attend a worthy Sunday Mass. Maybe he can seek a place somewhere nearby or another church in his region where at least a Novus Order mass or a Latin mass is celebrated worthily.
So he has to seek this possibility and make the sacrifice of traveling. We traveled 70 miles for Sunday Mass. 70 miles in one direction and another in coming back. For me, it was one of the most beautiful experiences in my life: the trips to Sunday Mass. And then all your life you will be fascinated by its importance. In this case, I would suggest that the father should do this, even if he cannot do this every Sunday but at least once a month or twice depending on the distance.
Dear visitors of Gloria Dei and all who have already written or who will write a personal message to me. I am grateful for your attention, your kindness, for your spiritual support and especially for your sacrifices and prayers for me. God may reward you!
