Is it obligatory to re-establish contact with an abusive father who deals in usury and treats his children harshly, in order for God to accept supplications and acts of obedience, or is severing ties with him better? And is there another solution?

What has been mentioned about the father regarding consuming usury and ill-treatment does not strip him of his fatherhood nor invalidate his right to dutifulness and maintaining ties. The obligation to honor one's father never ceases, and severing ties with him is a grave sin. Allah has commanded honoring even a disbelieving parent who strives to make their child commit shirk (definition), as stated in His glorious verse: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with appropriate kindness."

The duty is to end the estrangement with the father, then try to advise him gently and kindly. If he does not respond, then fulfill your duty of dutifulness towards him and pray for his guidance. Undutifulness to a parent does not prevent the acceptance of supplication or the approval of deeds. One must repent to Allah and strive to honor and treat their father well, and beware of abandoning Islam; for true comfort in this world and the hereafter lies in following its teachings, as Allah Almighty said: "Whoever does righteousness, whether male or female, while he is a believer - We will surely cause him to live a good life."