You raise some serious issues. If your daughter is not actively suicidal with a plan, an emergency room likely won't admit her. If she is actively suicidal, her age is on no consequence. However, if she is unstable and needs medication adjustment, that can be enough for admission, but the doctor prescribing the medications has to make that call. He can petition and certificate her for admission. Maybe leaning on him a bit would help.
The other question is, is your daughter compliant with her medication? If she is not, a hospital may feel she presents too much liability to accept her as a patient (as sad as this is, it is the unfortunate truth). The other question is does she have any inpatient psych. days left on her Medicaid? If she does not, she is considered to have no funding. A hospital would have to apply for emergency funding and/or she would have to be admitted into a state hospital. Lastly, in most states free standing psychiatric hospitals won't accept just medicaid, they want a supplemental insurance with the medicaid. However, a medical hospital with a psychiatric floor will accept just medicaid.
Allocation of mental health benefits and resources in this country stinks. I hope you are able to find her the help she needs.