Long-time lurker looking for advice.
Background, as to not to drip feed: DD is 6 weeks old, first child for DH and me. My family lives overseas and we like them, DH's family lives 45min away and "it is complicated". We go NC when MIL goes full-on narc but otherwise, have a polite visit every 4 to 6 weeks or so. They are not allowed to babysit and never will be.
While family support is limited, we have great friends who support us and are our part of our family. DH's "childhood" group of friends includes one woman, let's call her Abby, who became part of that group because she used to be BFFs with DH's best friend's girlfriend. I say used to be, because best friend's girlfriend hinted to us that she has outgrown the friendship but doesn't quite know how to deal with it. Abby is 28 but has never quite gotten past the teenage "we are going to be best friends for ever and ever" stage, which means she is not noticing the otherwise difficult to miss signs that the friendship is on its last legs. Not my circus, not my monkey, and naturally, we are staying out of this.
Abby has been babycrazy all her life (you can see where this is going) and wants nothing more than to get married and have children. She only ever had one boyfriend in her early 20s, which lasted for a couple of months. She does not date casually, which obviously is a perfectly fine choice but I imagine it makes it more difficult to find someone. When DH and me got together, I sensed some slight jealousy but decided to ignore it. I knew that DH asked her out once but nothing came of it because she seemed unenthusiastic and he didn't want to pressure her. Even if they did have a thing in the past, I wouldn't care, so really no reason for him to lie and she confirmed his story. When we got engaged, her response was "He asked me out first", eventually followed by "congratulations". I am not easily threatened, so at my end I just find it mildly annoying.
DD's "godparents" (we have an outing non-religious name for them) are DH's best friend + girlfriend and my best friend + her partner, who live a few hours away.
The Situation: We always used to have gatherings at our place, as most of that sub-group of our friends works in the city we live in, but lives just outside of it. It the most practical option. Now that DD is here even more so. We also want her to build a relationship with her godparents, as these four people really are like family to us.
The issue is that as soon as Abby hears someone else is here - even if it just DH's best friend stopping by to say hello and have a quick pint with DH on his way home - she will be over like shot and trying to babyhog (which we stop). She thinks she knows what sort of mental stimulation DD needs because she is a primary school teacher (I have a PhD in Developmental Neuroscience...still don't think I know what is best for someone else's child). She keeps talking about all the things she will do differently when she becomes a mother (like be a SAHM - which just isn't for me and that apparently makes me a substandard mother 
). She gifted us mountains of Disney stuff, although we have repeatedly told her we have got everything we need and want (she is really into Disney - I have no strong opinion on Disney but I am slowly getting to the point of hating it...). All of it plastic (toys) or high in polyester (clothes), which I don't really want to have near a newborn in these masses. Breastfeeding in front of people (in my living room, discreetely) was apparently something "she had always expected of me", because of my promiscuous past. I told her I am glad she knows that sexual exploration can make a woman more confident and comfortable in her body, and recommend she gives it a try.
And of course, there is the judgemental look and silence when we do something in relation to DD she does not approve of, and generally ruining the mood. The bottom-line is that she is probably jealous of me/us/"the life she could have had" and cannot hide it well. Normally I would just repeatedly put her in her place but I am lacking sleep.
The Question: Would I be unreasonable to ban Abby from our house? At least for a while?
I honestly have to ask. We usually have an open door policy. My hormones haven't quite calmed down yet and I don't have any shared history of "going through good and bad times together" with her, so I am not sure if I am being unfair. Neither does DH, technically, but I don't want to rip "his" group of childhood friends apart. DH feels similiarly but hopes that his best friend's girlfriend will finally cut Abby off, so that we don't have to do anything. He would support me either way but I am not sure if banning her might not be a little over the top?