We found out my step daughters mother had made up a you tube account for her at her house, we also found out that my step daughter wrote?

a "famous you tube gamer" an email. Me and her father are very upset about this as she is only 11 years old and is too immature for such things. Her mother said we were being insane because I gave her daughter a facebook and an instagram account that I know the password to and can monitor! she said if we can do that then there is no reason she cant have a you tube account that she monitors but my step daughter is emailing these gamers and this does not sit well with us, I want her mother to shut down the you tube account and I dont think we are being insane by letting her have a facebook or instagram those are both much safer and I monitor them!