Hi my sweet! Aahhh yes, the parental conundrum.........there are two scenarios.......they will be accepting and unconditional, or they won't. be prepared for it to swing either way.......
If she is the perpetrator, in a way, for this to manifest itself as borderline(as my mother with me) then she may get extremely defensive and will deny it. Especially as you said that she will probably research it for the symptoms and cause. Some parents just don't "grow" past the illness and refuse to accept it. My mother and I divorced for 10 years and my father stood beside me even though he had no clue what was going on. He tried to understand, but you know my opinion on getting others to comprehend....they cannot.
My mother, till this day, denies that I ever had Borderline. Although 15 years later, she has admitted to not "being the perfect mother" Ha! Yep, thats all i'll get from her. I don't need her to "confess"........I have already forgiven her. For me......
babe, there is no clear cut answer.......you either shout it from the rooftops or you put a cloudy "patina" over it. You don't have to spill your guts straight away.......at the end of the day, you are the one suffering, sacrificing and healing. Remember, it is a precious journey.......you get to choose who you share it with. And if you share it and they don't get it, or get hostile or think your a bad parent.......that is their experience, not yours and you walk away from the negativity.
You are number 1, forgive them for their flaws and the more resolve you show in your value system, the less they can hurt you. Eventually, they will come round. Being a mother and good person does not rest on whether your parents accept the dx.
You must find great courage in this to protect yourself, till this day, my mother is still the one who triggers me the most.......but to have her in my life(which is my choice) I have had to learn to unconditionally accept that this is the way that she is. But she doesn't frighten me anymore, she just makes me angry sometimes. Her value system is different to mine. Took a LONG time to get to this point. I do not need her to validate me anymore.
You take care my sweet........you are a proud person who is fighting the good fight.......be honourable in the process and rise above all that threaten to bring you down.......be still and breathe and others will follow......
Let us know how you go........

