I don't know how old your mother is. If she's elderly, maybe she doesn't want to travel alone. That would make sense to me.

Even if it's not what you were expecting, maybe it won't be too difficult, since they won't be staying in your house. See some tourist sites, eat some meals. The conversation may even be easier, since they're likely to talk about their traveling experiences and you get to listen a lot.

If she wanted the friend to stay at your house, I'd say that was pushing it, since your place is small, but you won't have that to deal with.

But yes, my mom might bring a friend. She's old enough now that she might prefer not to travel alone.