A similar question was first addressed by the rishonim quoted in the beis yosef in even haezer 165 -
ובספר המצות כתב שאם יש לו אשה אחרת שכופין
אותו עד שיחלוץ בסמ"ק אם יש לו אחרת מנדין אותו בהדיא עד שיחלוץ -
Smag - when hes already married, we force him to do chalitza.
Smak -we excommunicate him until he does Chalitza. This is in a case where the Yevama DOES NOT want to be a second wife, and without her consent we force him to do chalitza.
If however the Yevama DOES want to marry the Yavam (in spite of the Yavam having another wife) the Shulchan aruch E.H. 1:10 paskens
רבנו גרשום החרים על הנושא על אשתו אבל ביבמה לא החרים
Since the mitzva of yibbum precedes chalitza (indeed that is his opinion E.H 165,1 as opposed to the rema) takonas rabeinu gershon (not to marry 2 wives) is overridden by the Mitzva of Yibbum to be able to marry 2 wives as long as the yevama wants. this is based on the principal that a Minhag cannot override a Mitzva.
However the Beis Smuel in E.H 165,1 Brings the Teshuva of the Rivash 302 (14th century Sefardi Rishon)
אם יש לו אשה לכולי עלמא מצות חליצה קודמת
למצות יבום -
If He already has a wife everyone agrees to do Chalitza instead of Yibbum,
Though the Beis Shmuel seems to think the reason for this is because the Rivash was not sure whether the Mitzva of Yibbum is preferred or the mitzva of Chalitza is preferred. He quotes the Mahari Lebeis Levi who says only if there are other reasons e.g she doesn't want to do Yibbum, she or he are too old for each other, he doesn't have enough money to house/support the second wife only then do we force him to do chalitza on this potential 2nd wife.
In conclusion it would seem in a sefardi community that permits polygamy (probably doesn't exist anymore because polygamy is outlawed in most countries) that as long as the woman wants to do yibbum and criteria above are met, even if the existent wife protests she is stopping the husband from doing a Mitzva and therefore she giving him bad advice which he doesn't need to listen to (a bit like telling her husband not to do his tephilin so that they can earn more money through extra work time).