What is the ruling on communicating with one's father within limits to prevent problems, knowing that he deals badly, fabricates problems, and does not answer calls if his demands are not met, and he has relationships with many women? And are the children held accountable for the father's sins?

The questioner mentioned two matters concerning his father, and if they are true, then he is indeed doing wrong:

First: His harshness, cursing, reviling, and abandoning his children if they are unable to do what he asks of them. This is surprising behavior. He should be advised to be patient, supplicate for him, and counsel him kindly. If he does not improve, it is permissible to maintain contact with him within limits to avoid problems, without severing ties completely.

Second: His engaging in sinful relationships with women, which is illicit cohabitation (makhādanah) that Islam has nullified and forbidden. Allah Almighty says: "marrying [them] and not [being] one of sexual licentiousness or taking [secret] lovers" (Al-Ma'idah: 5). No one is held accountable for another's wrongdoing. Allah Almighty says: "And every soul earns not [consequence] except against itself, and no bearer of burdens will bear the burden of another" (Al-An'am: 164).