You just have to be open and honest. To the other Moms that do that.
Say you don't have the budget to pay for all the happenstance activities.
Say with a pleasant face and tone of voice being an only parent is busy... you don't have extra hands.
I would.
I have 2 kids. I have LOTS of play dates for them at our house and sleep overs. And if my kiddo tells me that they want to invite their friends over, I say, right there, that either it is 1 friend or none.... Mommy is tired this weekend and have lots to do etc. and they have homework etc. I say it. To my kids. I don't pad it. I don't feel guilty of it.
And, if I simply cannot take them out and pay for it/their friends, I SAY so. TO MY KIDS, and their friends. And I tell the Moms too. I say it in a normal everyday voice. It is just life, after all. And kids, well my kids and their friends, understand. And the Moms understand too, when I tell them. I say, everyone has a budget, after all.
I ALWAYS, tell my kids... how many kids or NOT, they can invite.
Always.
They know it. And they don't argue about it. I always TELL my kids, my thought process about it, so that they understand life and that, there are other things to think of too.
And if I am just tired, and don't want any kids here, I say so too. I say to my kids "Not this weekend. I'm tired and want the house to myself."
And if a Mom asks favors of me... and if I cannot or simply don't want to... I SAY so. Right, then.
And I don't feel bad about it.
I just say I have time constraints, or am busy, or simply can't.
If you don't speak up, then you will continue to be, resentful about it.
Or just tell them you are a single parent and have lots to do and juggle.
Since they don't even consider that.
Or they are taking advantage of the fact that you only have 1 kid. Therefore, they think they can have you do more and have more kids at your home... because, you only have 1 kid, compared to them and have less to do...just because you have 1, kid.
And that is not, right. Nor polite.
Just speak up.
And TELL YOUR DAUGHTER, yes or no, to play dates.
She is old enough to understand.
Per reciprocation of play dates. Well, not all parents do. Again, I have lots of kids at my house all the time. And most of the time I don't mind. But, at no time, do I "expect" the other parents to reciprocate. I don't have play dates for my kids, JUST so that, others invite them to their house. Some people just can't handle play dates at their house, or their house is small or messy or whatever. Or they have a fussy Husband who doesn't want kids at the house etc.
Also, you can make play dates a pot-luck. In my locale, the other Moms of the invited kids, always send something over with their kid. Be it snacks or food or drinks.
And if I don't have a feast to feed them all, I say so, too.
But the kids still have fun.