It's been three years since our rescue dog became part of our family.
The dog we got from the shelter has been with our family for three years now.
ーIt's been three years since our rescue dog became part of our family.
「保護犬が家族の一員になってから３年経ちました。」
It's been three years since ... で「…以来３年になる・３年が経った」と言えます。
rescue dog「保護犬」
became part of our family で「家族の一員になる」
ーThe dog we got from the shelter has been with our family for three years now.
「シェルターから引き取った犬が私たち家族の元に来て３年になります。」
「保護犬」は the dog we got from the shelter のようにも言えます。
ご参考まで！
カナダ 
