Voluntary relinquishment of mother's parental rights versus court ordered termination of such rights?

Question Details:

My husband and I live in Michigan. He is the legal father of two children by an ex. These children (along with three others) were removed from their mother's custody over a year ago and we have a termination hearing coming up in a month. Her lawyer is pushing her to relinquish her rights. My husband and I were wondering what the legal difference is between termination by the court and her relinquishing her rights voluntarily (ie: could she come back years later and try to get them if she voluntarily gives them up)? Does she have to pay child support, etc?

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