How to back up...

How to back up two separate itunes accounts, from iphone6, onto pc WITHOUT combining them?

2 Iphone6s'

My Iphone has had an itunes for approx 8 years

My daughter has always had my itunes apple username/password on all of her phones. Now we have created her own apple id...She needs to back up (1st time) old phone (also iphone 6) that HAD at one time my apple id on it. But I deleted all of my info & put in her new info into OLD PHONE so we could back it up for 1st time in itunes we created for her. From that backup we hope to then transfer the info onto her new iphone6.

Everytime I try to do this,my itunes always comes up too, but even if I sign her into itunes with new apple id.

Please lmk if this can even be done. THX!!!