You should be able to discuss thoughts about suicide pretty openly, but when you show intent and/or a plan, your T will kick into a different mode. She has to do that. To do any less would be negligent. You might want to have a discussion about where she draws the line. The description of her saying if you mean what you said you have to go to the hospital seems a bit vague. A detailed discussion about thoughts vs. ideations vs. intent vs. plans might be in order.

If you really do have intent or a plan, the hospital probably is where you need to be for your own safety. I know you don't want to hear that, but it is the reality.