To get married is to embark upon creating a home together, one in which each spouse’s individuality should express itself in a way that contributes to the greater whole. Your question is but one aspect of that larger project. For that reason, it’s not only a halachic matter, and it demands real discussion between chatan and kalla.
Halacha does provide some parameters, though:
The overarching goal is to create a unified home life (Tashbetz 3:179). Therefore, a wife’s practice in personal matters can remain her own (Bnei Banim III:29; Si’ach Nachum 88), and when a husband’s and wife’s customs are not in conflict, there can be room for both.
When customs do conflict, the wife takes on her husband’s. Many halachic authorities view this as obligatory, and the wife as akin to someone who makes a permanent move to a new place, who adapts their customs to the new locale (Iggerot Moshe OC I:158). Others argue that the husband, too, is in a sense changing locale, and thus view her taking on his customs as itself a matter of custom (Benei Banim III:29).
Rav Nahum Rabinovitch writes that a couple can choose to adopt some of the wife’s customs together instead of the husband’s (Si’ach Nachum 88). A couple pursuing this path should seek specific halachic guidance regarding the customs in question, their halachic weight, and whether a hatarat nedarim (nullification of the vow implicitly undertaken to follow prior custom) is required.
Additionally, a husband may not impose stringencies on his wife, especially with regard to halachot that apply primarily to her (Iggerot Moshe EH 2:12; ).
Putting the pieces together, a woman marrying a man with a different tradition need not change her personal prayers. She can immerse in the mikveh as her mother did, but would follow the traditions of her husband’s community on the laws of niddah that affect them both. Her rabbis and poskim remain in place for matters concerning only herself and can be consulted on other matters, though the couple should choose a rav, and a course of action, together.
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