OK, this is how I would do it. Keep in mind, there are two types of accounts with Apple and they both use an email account. The AppleID is what is used for AppStore, Music Store, Apple Music type purchases. The iCloud account is used for calendars, contacts, email and such. The confusion for a lot people is that many times, both of these accounts use the same email, so it's often used interchangeably, but they are separate.
OK, I'm assuming that your daughter and her mom would like to continue to use the mom's AppleID so that they can share purchases for apps and music. But I guess your daughter wants to have her own contacts and calendars.
So have your daughter create her own iCloud account using her email address. She can continue to use her mom's AppleID for apps and music.
On your daughter's laptop, she would authorize her iTunes with her mom's AppleID. Then she can copy over the songs that she wants from her mom's iTunes to her own. Then she would sync her iPod to her iTunes.
This is how I have it set up with my account and wife.
Alternatively, you could set up Family Sharing, but I know very little as to how this works.