Okay, bear with me, this is NOT a "deregister your phone number from iTunes" thing. If I get another canned answer telling me to deregister my number, I'll go nuts. Here is the issue, and please read all the way through before responding:
So what gives? HELP please! And Verizon, please no canned answers; look into this seriously.
Have them delete the contacts for you and your mom and the previous text threads for those contacts in their phones and re-add them making sure to save your numbers with just the 10 digits of your number. (No 1/+ etc.) That should fix the issue.