Are the questioner and her mother considered severers of kinship ties due to the disagreements that occurred with the aunt, and what is the supplication that the questioner can make to be blessed with a righteous husband and avoid the schadenfreude of others?

As long as the mother and daughter communicate and visit relatives on occasions, this is not a severance of kinship ties, especially if frequent visits cause disputes. Maintaining kinship ties is obligatory and not a reward. The true maintainer of kinship ties is one who maintains them even if they are cut off from him. As it is stated in the Hadith: "The one who maintains ties is not the one who reciprocates, but the one who maintains ties is he who, when his relatives sever ties with him, he connects with them." One must beware of envy, for it is forbidden and a cause of worry and grief. As for marriage, there is no specific supplication for it; one can supplicate with any formula. We ask Allah to bless the questioner with a righteous husband.