mom & dog -- her next to last dog

Mom bought a pure breed Cairn Terrier (Becky) & breed her once.  My sister & I both received one of her 4 pups.  Cairn Terriers are loyal friendly dogs but will not back away from a fight if pushed too far.  Mom loved Becky a lot but when she got out & we believe stolen she tried to replace her with a dog from the shelter.  Becky got out 2x & when approached by another human, she would roll over on her back expecting a belly rub.  The 1st time we hear her barking in a neighbors yard at night and this was after they denied seeing our dog.  We have had problems in our neighbor for years.  Dogs have been taken out of peoples yards.