Is limiting one's connection with abusive relatives to occasions such as Eids, illnesses, and condolences considered a severance of kinship ties, especially after attempting to advise them without success, and out of fear of their gatherings which involve backbiting, slandering, and bearing false witness?

The Shari'ah commands maintaining ties of kinship and forbids severing them, even with those who sever them. If some relatives backbite and spread slander, you must avoid these prohibitions and be keen that your gatherings are gatherings of goodness. If backbiting occurs, you must object and explain its prohibition, and redirect the conversation away from forbidden matters. If that does not help, then it is obligatory to avoid these gatherings, while still being able to maintain ties with them by inquiring about them and similar actions that do not cause harm or lead to forbidden acts. For the Shari'ah did not specify a particular method or measure for maintaining kinship ties; rather, the reference in this matter is to custom and varying circumstances.