IPhone – I have Messages in iCloud but messages still not perfectly synced

My experience is you cannot actually delete an iMessage once and have it delete elsewhere.

You can only delete the local cached copy of a message to suppress it being showed/stored on that one device. If you turn off iMessage and turn it back on, you will see the messages from iCloud come back whether you deleted a message or not.

I would check your address book entry on your mothers iPhone. iMessages can be registered to phone numbers, or email addresses. My guess is that because you're sending iMessages they are arriving under your email address on your mothers iPhone. Then, when she sends SMSs to you they go out under your phone number. So, check her iPhone's address book. Ensure that your entry has both your email address and phone number under the same entry.