Can't show care to family

I'm an empathetic person and feel very deeply but at the same time It's very hard for me to show care and concern with simple actions, and specially words and facial expressions to my family (started adolescence up to adulthood) even though they were very loving to me since I was a kid. I feel the care inside but feel soo abnormally awkward to express it and come off cold. The weird thing is I can show that side of me to friends or strangers. Anybody experience this?.. and I have mild BPD btw.. but most of my childhood stress was from schoolmates and neighbors. But I also never knew my dad and My mom stressed me out too as a kid with her constant outbursts to her sister for small stuff like getting me dessert once in a while or offering typing lessons but when it came to me directly I wasn't abused in any form and loved and cared for. Can anybody give me an opinion what is up with my brain?:D

Edit: And there are times I go verbal sadist on my mom for stuff other people wouldn't go crazy for, I feel really bad most times after but never apologize and we just always end up acting like nothing happened. Then when it comes to outsiders who are real assholes I'm very patient and hold my temper. This sucks, I want it to be the other way around but I can't apply this realizations in real life on a day to day basis:(