I'm going to give my partner an ultimatum to work on their mental health issues or leave our relationship.
Would you get a divorce if your partner doesn't do what you've asked?
If they agree to go to therapy we can stay together.
I'll be honest with you: I don't see that ultimatum solving anything. In fact, I see it causing more problems as most ultimatums tend to.
Unless they improve their mental health and work on their issues there's no way we can stay together.
It sounds like you're unhappy dealing with your partner's mental health issues. Do everything you can to support them, but you and your child need to be taken care of yourself. If the relationship won't work, them it may be time to move on.