"Mental health issues" is too broad a term. The issues would have to place the children in danger. From what you are saying, your ex has had these issues and has not been a danger to the child. Therefore, you would have to show how your ex is dangerous. Example: DUI charges when the parent drives the children regularly is a danger.
There are really two questions here: whether you should seek to change the custody order, and whether the circumstances constitute and emergency, which would prompt the court to make a temporary order before the normal process has been completed.
The answer to these questions depends on the facts, particularly the nature of the behavior, and the effect it has on the children. I'll give two examples. A person who is receiving appropriate treatment for his or her mental health issues, which is effective in controlling their symptoms, might be a very good parent. Another person whose symptoms are not controlled might be doing something that endangers a child.
You should sit down with an attorney and explore your individual circumstances in detail.
This is not intended to provide legal advice about your situation - just a few casual remarks about a legal question. We are a debt relief agency helping people file for bankruptcy.
Most judges do not like to hold emergency custody hearings on any thing less than a real emergency- i.e., imminent danger to your child. You haven't stated any facts other than a general mental illness, so it is difficult to advise you. If, however, there are circumstances where your child's health and safety are at risk, then absolutely, you should seek emergency help with an attorney that does custody work and understands these issues.