Hi OP — I say this for you to reflect on, as only you can answer these questions.
As an only child, your daughter will be used to your full attention, and you’re used to giving it. Could it be that when your friend visits, she feels interrupted a lot? Your daughter may also struggle to share you, so she stays close when you have company.
Speaking as a mum of three (and in a friendship circle with mums of 1–3 children), we’ve noticed that friends with one child can sometimes be so focused on them — understandably — that others feel sidelined. One of our friends with an only child often talked so much with her daughter, even at coffee meetups, that another friend once said she felt like the “extra one.” She has no idea she comes across like this.
For example, I recently walked with this friend and her daughter after a club. She invited me along, but most of the walk was her chatting with her daughter. When she did start talking to me about something- her daughter got annoyed and interrupted and the conversation went back to her.
What I’m getting at is: if you only see your friend a few times a year, do you set the expectation with your daughter that “this time is for mummy and her friend”? Or is it that both of them end up vying for your attention?
It’s not that your friend shouldn’t engage with your daughter — you’ve already accepted that as part of your friendship — but perhaps it’s worth reflecting on what the dynamic feels like for her. I also know other mums of one child who balance this really well, so it is possible to keep both relationships nurtured.