If the mail for your child is coming to your address and the child is still a minor and lives at home then yes you can legally open the child's mail.
Nobody is gonna know about you opening your child's mail anyway unless your child gets mad enough and calls the police.
But even then you're not gonna get into trouble for opening your child's mail when you're still legally responsible for your child.
I've opened my children's mail all the time to see what it is but if they got a birthday card I would always wait and let the child open up the mail.
Because the birthday card usually included money from Grandma and Grandpa and other family members which made the child so excited.