No one can tell you what you SHOULD do - or think badly of you for weighing it up, because ultimately we have to live with our own decisions and therefore you have to feel comfortable with whatever you decide.
Here however is what I, as a trainee clinician would do, when confronted with two patients both needing my attention.
I would respond to the the needs of the most vulnerable patient first, because they are the one most likely to suffer serious harm from any delay or lack of response. The other patient may deteriorate a little, but as their condition is not as pressing I am hoping to be able to repair any damage done by the delay when my first patient is properly stablilised.
Now apply that principle to this situation. Here is my analysis, yours may be different and that's ok.
I would say that your most vulnerable person is your SO - who is going through a process that I have seen unhinging many many people. The frightening statistic about trans suicide becomes even more telling when you realise that many of the suicides are not those who are repressed and still in original gender, but those who are transitioning and being treated. It comes about as the inevitable consequence of being abandoned and cast out by loved ones, and treated by pretty much everyone daily as objects of scorn, freaks and pariahs.
Unless I am very mistaken about the situation your SO desperately needs your unequivocal support just now - which under this circumstance, if no accommodation can be reached, probably means not going on this occasion, and later explaining to your family, that while you love them, they do have each other for support. Your SO potentially doesn't have that support and thus needs you more than they do at this very vulnerable and important moment in life. Your family will be sad if you don't go, but they will still have a good time. Your SO will not have a good time if forced to go and forced to hide who they are becoming. It will be just another little chip at the boulder, which might eventually even crack.
Later I might also ask them what they think their Lord would have done in this situation. Would he have befriended and welcomed the outcast, or would he, like the religious people of his day (pharisees) have turned them away from his table? I would try to explain the pressures a little and ask them how they would feel if your SO had felt abandoned, cracked and became one of those statistics? I'm sure the answer is that they would be mortified, but unfortunately most people don't see that possibility until it is too late.
I feel very sorry for you. I'm sure your family are good people, but unfortunately they probably don't understand what is happening and in their enthusiasm to uphold what they perceive to be the rules of their faith they have, like so many, perhaps lost sight of the compassion which is supposed to be its most important principle. Sadly it is falling to you to be the pastor, educator and guide.
I am so glad you are thinking this through and I wish you a positive outcome.
