How can iMessage send from my old phone number that doesn't have service anymore?
I think there is only a solution for this and is the one that you have found on internet. 

More precisely, no matter if you are not using you iPhone or even your number configurate to iMessage in your phone, if you mom's phone marks the message from iPad under your name this mean only one thing and the thing is that the iMessage account on your iPad is configure with the same iCloud account (email) that you have on the iMessage of your iPhone.

You can always change this settings. The interesting thing's for you is to figure out who did this ;-)