I am tempted to ask my child what goes on in my co-wife's home. Should I hold back?

Yes, hold back that urge, because investigating through your child only adds to your unease and traps the child between two homes. Information gathered this way is usually interpreted badly and fuels suspicion rather than bringing peace. If there is something you truly need to know for the child's welfare, ask your husband directly. Shift your focus to what you can control: your worship, your children and your own home. Every time you feel like asking, seek Allah's forgiveness (istighfar) and steer the conversation to the happy things in your child's life. Keeping yourself from investigating is a gift of peace to yourself. See co-wife relations.