You have two serious problems. None of which are your strepstep-son/daughter. The first is you. You accept this behavior, your allow for it. YourYou're supportive of it. Now that doesn't normally sound like a bad thing, but it can be. Especially when the parent is not. It's his mother's call, rather the family unit supports Emily in this or not. And clearly, the mother does not. Let me be clear here. To the mother, the son is talking about self mutilation, destroying their body, causing massive self harm, and going down a path that will make them an "outsider" in almost every situation. And you, her boyfriend, are coming off like, "sure let me go find a chain saw and we'll get started".
Now to be fair, as an outsider, I know that's not exactly what your doing. But your girlfriend has a set of values, that Emily is deciding to break. And rather thenthan support your girlfriends values, youryou're "siding against her." That is a very bad thing. You should support your girlfriend, even if you disagree, and then try to change her opinion privately. This is difficult.
Now, starts the "what you can do" phase. First, ALWAYS support the mom. She's the parent not you. It can be hard to do when you care about someone, but if the mom wantwants to send her to some "horrible camp" then you should go pick up brochures. That being said, in private, you can try to talk to your girlfriend, and while still being supportive, get her to understand your point of view. Pick small battles. Try to lesson the impact. But always be supportive.
For example. Hey, I know you want to send him to camp for this, but I think it's a bit more serious thenthan that. I don't think those kinds of camps are going to work at this point. Why don't we get him to talk with a shrink that specializes in gender identity issues. Then we can see how far this really goes.
Then you can find consolingcounseling that fits the situation. Some consolerscounselors will try to talk Emily out of it, some will try to help her down the path. Again back up mommy on this one. Any consolercounselor is better then a camp situation.
Refer to Emily as He, and use his name. Explain that until the "job is done", he is still a boy. And he is expected to act/dress like one. Explain that it's his mother wish that he do so. Try to emphasisemphasize that this undertaking is a long and hard process that will take several decades. It's not an afternoon under the knife and some pills. Try to explain that in order to really judge if he should make this kind of change he needs to be "in a good place" with himself first. He needs to accept that he is a he. And that he wants to change that fact. The consolerscounselors will likely tell him the same.