What rights does the other parent have if a temporary care and custody agreement is signed without their consent?

A temporary care and custody agreement is between a parent and the society - it doesn't require the other parent's consent to be valid, since a society can enter into one with whichever parent has care of the child at the time. That doesn't leave the other parent without rights, though. The other parent can ask the society directly about the arrangement and about arranging their own access (the CYFSA's own term) to the child during the placement, and can raise the existence of the agreement in any ongoing or new family court parenting case, since it's a material change to the child's living situation.

If the other parent believes the agreement isn't in the child's best interests, or that the child should be placed in their own care instead of the society's, they can raise the issue with the child protection court, the family court, or both, depending on what's already before each. Because these situations can move quickly and involve two different legal processes at once, the other parent should get legal advice promptly rather than relying only on informal conversations with the society.