Rachel is a very proud and refined lady to begin with partly due to her canon father most likely and the fact she is immortal might have given her better prospective over time I imagine raising her would not be a hard thing at all to do but I believe her mean streak she has could present some problems since I have one at times myself with certain aspects of that in both of us and I'll be honest while she knows a lot she can get ahead of herself on rare occasions would probably challenge authority when she seems appropriate though when she has in canon it was within reason. I'd teach her all the essentials of etiquette and proper discipline with some of the more positive aspects of my nature and philosophy but I'd want her to find her own way and not make the mistakes I have.

One thing I have to consider Rachel as a human might be much different compared to a vampire, I don't know really anything before the vampirism bit of her most is unknown to me so mortal Rachel could be much different.

If it's from infancy it's a bit hard to imagine her growing up with the same personality, especially since much of what made her who she is can be clearly and directly linked to her family members and the role they played in her upbringing. That said, she's been characterized has having a very strong connection with her father, which could be a good thing but alternatively might be hard to live up to. It'd be a bit weird, but I guess I'd try to be a good dad?