Regardless of the frequency of visitation, if you marry your BF, then your family will be as much her family as he is. It's a package deal. They should treat her just as they would a blood relative that only sees them a few times a year. If they treat her differently, it may make her feel like an outsider and uncomfortable. It will also be more important if you have children with him.

Depending on how her mom feels about it, you might even have them send cards & gifts to her directly on her birthday & Christmas if she isn't with her dad. I would think that she would feel special and cared about to know your family is thinking about her. I can't imagine why a parent would have a problem with as many people caring about their child as possible but sometimes they do, so check with her first.

Maybe when you get married he can start spending more time with a kid. Once a month with 8-year-old child is not enough. Is her mom OK with infrequent visitations?

I would say that you and your sd could have a great relationship. You do not see her enough to have the stress of day to day life in your relationship, so that gives lots of room to form a friendship with her. As far as family, your family should treat her as family. It is obvious that they will not be as close to her as they are to other family, because they do not see her often. But, it is important to make her feel like she belongs.

As a kid who was in a stepfamily situation I know how it feels to be excluded. My sd's family treated me as their own and I always felt so happy with them. My sm's family treated me way different than my half-sis (sm's and dads child). I would be there for holidays and be the only kid who received no presents, that hurt. I love my sm, she was always wonderful to me. But her family was not as thoughtful. As an adult I can see that it was just stupidity on their part, but as a child I was very sad about it.

Hi Nougat!
I also have a BF with an 8yo (only his is a boy). I call him A__ on here because "my BF's son" is pesky to type out all the time.

My BF and his ex both work some odd shifts, so sometimes it will be two or three weeks between when he has A__, but sometimes it will be two weekends in a row, three or four days on each. Usually it's a night or two each weekend.
So, I see my BF's child a lot more than it sounds like you will, but I know about the long gaps and that they can make things more awkward.
One thing I try to do with the long gaps to provide a little more consistency "Next time you and I see each other, we'll read this book / watch this movie / teach you how to fall so you don't hit your head on the ground when we wrestle / go to my lab to look under the microscopes / extract DNA from bananas / etc" and then I make sure to do the planned activity next time we see each other, whether it's later in the week or three weeks from now. A__ seems more relaxed when he knows what the weekend will hold before he arrives. Plus, these are good bonding activities for us.

The closeness level depends on the people involved - you, her, your BF, her mom. A__ has a HUGE heart and loves like you wouldn't believe, but other kids are more reserved. I love kids and have a nephew his age, so getting to know him was pretty easy for me, but for shyer people or people who are less comfortable with kids, I think it's harder. My BF thinks it's important for me and A__ to get along (to be frank, because it makes his life easier) and that helps a lot because he facilitates our relationship. A__'s mom is quite dismissive of me, but doesn't seem to mind my interactions with her son, so I don't worry too much about stepping on her toes.

I like the advice someone gave of checking with BM before taking your BF's DD along to your family outings. I, luckily, didn't have to do that because she was fine with my BF's exGF's family, fine with my BF's SM's family, takes A__ along to her BF's family functions and has told my BF that whatever they want to do when they're together is fine - by past precedent, it was OK by her.
Your family should be accepting of her and treat her like any of the other N&Ns. Although, of course they have to get to know her! If they exclude her or treat her differently, I think you're perfectly within your rights to tell them to smarten up.
A__ has been to several of my family gatherings. He and my nephew play together, he sits with the other kids for birthday cake, my family had presents for him to open at our family's Christmas exchange. They accept that A__ is becoming part of my family, and therefore becoming part of theirs.
My one brother and my one BIL don't really care for A__... but they also aren't keen on my nephew who's the same age and almost as high energy, so that doesn't really bother me. Plus, they're nice to him, so that's all I can ask!

As for how she close she gets with your family, I think that boundary is up to her. IMO, she has to be nice to them and treat them with respect, and if she's comfortable giving hugs and kisses or calling them Auntie and Uncle, then great.
A__ seems to be getting quite comfy with my family now. I noticed he took quite a shine to my SIL (my nephew's mom) right away - presumably because she provided cake and had the most interactions with him the first time he met everyone. After that, his level of interaction and affection seemed to correlate with whose name he could remember and who sat down on the floor to play with the kids.

Basically, my opinion is that as adults, you all have to open up your hearts and minds so that she's comfortable and secure getting close to you. She has to be nice to everyone, but should be allowed to set the pace in the relationships.

I have 2 SSs, ages 13 and 12, and have been married to their dad for 9 years. They live with BM 2 hours away, 4 hrs round trip. They visit about EOW, their activity schedules permitting. I hate to be pessimistic, but I would say that it will be difficult to form a bond with an 8 yr-old child that you see only once a month, simply due to infrequency of the visits and the fact that it takes time to form a bond with a child. After all these years, I am fairly comfortable and at-home around my SSs but we simply do not have a bond. I think they would feel disloyal to their mother if they had a bond with me. I hug them and tell them I love them, and they say nothing. They brought a Christmas gift for their dad, but nothing for me or their 2 half-brothers (my and DH's sons.)

I also have faced the issue of my relatives' treatment of my 2 DSSs. My parents were divorced and live an hour away. (My dad is now deceased.) I did not see my father that often, so obviously, the times when I saw him with my DSSs were even less. He and my relatives on that side of the family did/do not buy gifts for my DSSs at Christmas (the almost never saw them on Christmas anyway due to the short visitation schedule) or on their birthdays. My mother and her SO are closer to my DSSs because my mom and SO visit my home more often, so there are more times when they are around DSSs. Still, my mother treats them differently. For example, this year, my DSSs were there on Christmas morning and my mom gave several presents to my 2 sons and gave DSSs cards with $20 each in them. I am sure she spent about 3 times that on each of my sons. My mother is not the kind of person you can say something to about a situation like that without causing a fight, so I just let it go. Your parents/family may treat this child differently if you marry her father, but I think it is a little unrealistic to expect that your relatives who do not know the girl and almost never see her are going to treat her the same as your child who is their flesh and blood that they see frequently. I am not saying that is the way it should be, but I think it is frequently the way it is. In my case, I don't think my DSSs cared because 1) they like the gift of money anyway and 2) they themselves do not feel the same about MY parents as they do about THEIR GRANDPARENTS. That is just the way it is.