Under circumstances such as these, the state generallly comes in to place children in Foster Homes. If a relative steps up to take the children, the state will generally agree. Otherwise, a guardianship may be necessary. Contact a family law or guardianship attorney with further details for a more definite answer.
Of course Mother has a say in where the children are while she is in the hospital. Ordinarily they would be with the Father, but if that is not feasible then another responsible adult/ relative is fine. CYS may check on the situation, but if the children are well cared for they will not intervene. An order of court may be necessary giving the caregiver custody or perhaps guardianship.
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