Parents introducing us to their new partners is almost always uncomfortable. Everyone tries to act nicely, but it's very hard to get along on the first day. And for everyone dating someone with a son or daughter, this post is also relevant to avoid some things that are far from ideal.
I think that when we're nervous about somebody accepting us, we tend to be far too nice, even to the point that it's ridiculous, and that kind of hospitality, when it's inside your own house, the one you're used to being in since you were little- can make anyone uncomfortable. It is absolutely tiring to have someone asking you if you need anything or telling you instructions about how to behave in the house.
Plus, if you are the partner of someone who has kids, don't act like a stepmother or stepdad right away because it's not your place to assume that role; when it happens, it's more like something that's given to you with time and trust. Either way, you're never going to have that role with a 30-year-old, like in this story, so you can use some common sense and you'll be fine.
In my opinion, this girlfriend was very nervous and started acting ridiculously, or she literally didn't know whether the daughter knew the house, and she started acting like it was hers because she stayed there very often, and that's definitely more on the father's side of responsibility.