Make this about sexual sin not about homosexuality. God calls us to be pure and the unmarried to be celibate. Which is why all sexual sin should be treated equally. All sex outside of marriage is practiced sin, which is what this is about, practiced sin and not wanting to support it or have it under your roof. But do do this you must be standing on solid ground.
Check that there are not other family member doing practiced sin, especially sexual sin that is being overlooked. An example might be that there is someone you know who watches porn, or a married man who sexually harasses his co-workers or a heterosexual couple who live together without being married.
So first check your house and the plank in your own eye honestly.
Matthew 7:3-5
3 “Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye? 4 How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye? 5 You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother’s eye.
Then if you can honestly say no or you do not know of any, then you can move on.
You can then tell your niece that you love her and always will and that she is welcome to come over by herself anytime, but that you cannot condone sexual sin, that God calls the unmarried to be celibate no matter who they are attracted to. Having her partner over condones it silently. Which is something you simply can't do. Jesus did not condemn the woman caught in adultery he forgave her but then he said "Go sin no more" and he expected her to go sin no more.
If she does as God wants for her, which is to remain celibate then you will support that fully, but so long as she continues in practiced sin (and be sure to indicate this would be the same if her partner was a male) then they may not come together as a couple under your roof. It isn't about who she is attracted to, but what she does with that attraction.
James 1:15
Then, after desire has conceived, it gives birth to sin; and sin, when it is full-grown, gives birth to death.
What you do depends if your niece is a born again Christian or not.
Also you can only take this stand as a Christian after a good hard look at yourself and the rest of the family who profess to be christian and only if you truly believe that a heterosexual couple living together, adultery, pornography watching is as sinful as her and her partner and only if you take the same stand for all of them. Anything less is hypocrisy. This is not an easy hill to die on and die on it you may do.
1 Corinthians 5:11
But now I am writing to you not to associate with anyone who bears the name of brother if he is guilty of sexual immorality or greed, or is an idolater, reviler, drunkard, or swindler—not even to eat with such a one.
If she is not a Christian then that does not apply. Still have this talk to her and let her know why you are against sexual sin. Again do not make this specifically about homosexuality but rather immorality in general and then have everyone over including the partner and treat them as you would anyone else. Remember it is God they are sinning against not you. Pray for them as you would anyone else.