Is it permissible for a man to stipulate to his fiancée that she not visit her maternal uncle's house—his former divorced wife—and suffice with phone communication, and would that be considered a severance of kinship ties? And is it permissible for him to also stipulate that she cut off communication with her paternal cousin who harmed him, and is maintaining ties with the paternal cousin obligatory, and is it permissible for him to order her to sever them?

A woman's connection to her maternal uncle is obligatory because he is a mahram (definition) (unmarriageable kin). This connection does not necessarily require visiting his home; rather, communication and contact suffice. There might be no harm in preventing her from visiting her maternal uncle's home after marriage and her engagement with marital duties. As for the paternal uncle's daughter, she is not mahram, and some scholars do not obligate maintaining ties with her. The definition of mahram is any two individuals who, if one were male and the other female, would be forbidden to marry each other. This is not the case for the children of paternal uncles and aunts, and maternal uncles and aunts. Some jurists hold that the only kin with whom ties are obligatory are the mahram, and this is the view of the Hanafis and a less common view among the Malikis. They cite as evidence the hadith (definition) prohibiting a man from marrying a woman alongside her paternal aunt or maternal aunt, out of fear of severing kinship ties. The second view holds that maintaining ties with all kin is obligatory, whether mahram or not. Therefore, there is no harm in preventing your wife from visiting her paternal cousin. As for the maternal uncle, if you feel secure regarding your wife and can accompany her to visit him, that would be better. Otherwise, communication suffices, while being wary of excessive jealousy and negative assumptions.