Hugs to you in this difficult situation.
Tread lightly. Speak with love, not demands. Your immediate goal is connection and trust. Demands for immediate action the moment you arrive might backfire.
If you can attend a therapy session with someone in your hometown before you get on a plane, this might help you dial back on your emotions.
When you see your daughter, You want to present yourself as calm, loving, and trustworthy. Meet her where she is, at least initially. If you can document her thoughts and actions in the first 24 hours, you can better understand what she is dealing with. Or at least have real data to present to a therapist or ER personnel.
You dragging her in an ambulance to ER is probably a one shot chance. Do not waste it—be prepared with facts, recorded words and/or video to back up your claims. You do not want her to be able to explain away your concerns, or turn on you and make YOU into the bad guy.
Write out your notes now. All the suspicious and concerning actions and words. Some sane people believe and act according to numbers, astrology, religious beliefs, and that alone may not convince a therapist or judge to commit her.
Find out laws/rules of non-voluntary commital in the state/county/city your daughter lives in. NAMI might be able to help you. Knowledge is power. Know what level of Proof you need to take legal action to help your D against her will.
Do communicate with her current therapist immediately. You can tell therapist everything, even if he/she can not respond.
Do you have contact info for the family she nannies for? That part of it is tricky—do you contact with suspicions, risking hurting your Relationship with your D? But not giving them info could potentially put children at risk.
Counselors are trained to ask questions and rate a person’s risk to themselves and others. Not sure if you can research and find this type of info online. But this kind of logical step is the unemotional path you want to use with your D.
It will be difficult, of course, but you need to steel your emotions and work on practical and logical ways to interact and be of help to your D. This is where speaking with your own therapist before you get on a plane is going to prepare you to fight For your D instead of fighting WITH her.
This is going to be hard. But you will not regret getting on that plane and spending time with your child. Gaining an understanding of her condition will help you help her.