If you’ve tried to avoid a family member for years and aside from being geographically distanced, your only method to do this is to not give out our personal contact information. How would you feel if, TWICE, your own mother has given this person your information and then bald faced lied to you about it saying she wasn’t the one that did it.
Unfortunately, unlike some other members of the family, you can’t choose these.
Just as well really. Most of us would choose other parents, and so would our own children!
Let it go.
I’d figure that my mother isn’t going to change so I’d stop asking her if she is the one giving out the contact information. Why put her in the situation where she’ll want to lie to protect herself.
Assuming that it really IS your mother giving out the info and you REALLY need to avoid the other family member then I guess you have two choices:
You either accept that this family member will know where you are and always let the phone go to the answering machine/voice mail unless you recognize the number. And you never answer the door unless you recognize the person. And you get a dog with a deep bark.
Or you move and change your phone numbers and you don’t give your mother the new information. And you only email her from the library and call her from a pay phone (if you can find one.)