Sibling is unwilling to move mother to a memory care center that takes Medicaid?

Sibling is unwilling to move mother to a memory care center that takes Medicaid. my mother is in a memory care facility since the first of may. She was moved to a secure room the end of June that is more expensive (by $1000 monthly). The facility does not take Medicaid, self pay. My sibling is not willing to move my mother to a facility that does take Medicaid; therefore, leaving the balance of the monthly bill up to us to pay. By law do we have to pay? We do not have a say in where she is.