Are there ever any circumtances in which a parent can regain parental rights after signing them over voluntarily? Such as proof that the mother and adoptive father are not taking care of the child as they should?

Not really. If you relinquish your rights you no longer have standing to assert that they are not properly taking care of the child.

What if the state and children services gets involved?

While most likely you can not get them back, but if they are not taking care of the children, report them to CPS