I kind of imagine sares Meeting Pip's mother in the most unexpected way. It happened like maybe two or three years after Alucard disappeared, seras and pip were investigating a small gang of them vampires taking people from streets and draining them. The hellsing organization also discovered that a bounty hunter known as the black swan who was hired to take in the leader of the gang. Pip couldn't help but think that name seemed familiar, but he didn't know were. That was until he was the black swan in person and realized that was his mother. It had been a long time since he had been home, beside talking on the phone, so they had seen each other in some time so they were very happy to see one of another.
Seras, on the other hand, was in complete shock for a number. His mother looks quite young to be a mother
(she found out evie, Pip's mother, had him when she was really young). She was really friendly and sweet to seras after after finding out that she was the girl her little boy kept gushing about. even calling seras her future daughter-in law at one point. (I imagine evie has such a laidback personality, except if it comes to Pip's safety, then she becomes the definition of a protective mother.)
Evie loves seras even though she knows she is a vampire and that Pip is her familiar. (Evie pretty much says that she has seen worse). She is just relieved that her little duckling was happy. Evie would admit she did look into some info about seras as in she looked at all of the info about the girl seeing her son. evie also thinks the orphanage should have been more understanding and took better care of seras, especially after the events that happened to her and her family.
Evie didn't want to tell Pip about the family business. That until he was old enough to take the new well, and she especially didn't want Pip to think he was expected to become a mercenary like all the other members of their family. Only for his blunt grandfather spilled the tea when she had him watch Pip while she was on a job overseas.
The wild geese have met Evie, and a few of them actually tried flirt with only to be stopped by Pip glaring at them slightly, saying, "Don't even think about!".
I kind of imagine that Evie and integra get along quite well, maybe even have a bit of brief lesbian fling.
Lastly, I imagine Evie is of medium height, has long blazing auburn hair, fair tan skin, the same green eyes as Pip, a silver locket with a picture of Pip as a child, and another of her late husband, a black swan tattoo on her left shoulder, and all black fitted clothing and high heel boots.