My mom has her own Apple ID under my family sharing. On my phone it is combining messages that I am trying to send to her iPhone and her iPad. Same is true if I'm trying to message her from my ipad to either her iPad or iPhone.
What is being combined? You're messaging one person who has their own ID on two devices -- it is normal for two or more devices using the same ID to be merged together, depending on how you set things up. Surely you're not expecting two separate threads -- one for your mom's iPhone and a separate thread for her iPad, right?
If that's what you want, then her iPhone needs to be set to only receive iMessages to her phone number (not her Apple ID as an optional point of contact) and her iPad needs to be set to only receive iMessages to her Apple ID (not her phone number as an optional point of contact). She would also need to disable Text Message Forwarding on her iPhone to prevent those messages from being sent to her iPad.
But if I'm misunderstanding your concern, note that this thread was for messages of multiple people being merged into one thread (because they shared an ID). Perhaps if you explain your problem in a different thread you might get some answers (this thread is saturated, and appears to be unrelated to your issue).