No, you should not feel guilty. I have not stayed with dd at play dates (shudder at the word) since she was 6. If the person is a friend from school, and I know the mum from teh school gate then I am happy to let dd go without accompanying her, likewise her friends are happy to come here without their mothers even if it is their first time here.
So, you could not have known mum was going to stay and hence you cannot be expected to cater. Coffee and cake is plenty.
All sounds fine, nojustif maybe I'm reading too much between the lines, but it seems as if maybe you'd have quite like to have done lunch etc., just because it's fun... but you feel like like you need justification to do so - i.e. 'should' do lunch, rather than just doing it coz you wanted to, IYSWIM. Coffee, cake, etc. - all good, though,
9yo friend? I can't see how a 9yo would need her mother there, whether she had been there before or not. Coffee would have been plenty. Cake was polite. Girls given lunch. Give the mum lunch... Not a chance, you invited the dd not the mum. And certainly no to tea. Don't feel guilty. You did the right thing. And the politest thing.
I think she was being unreasonable if she didn't bring the cake, there was no need for her to stay all day (I saw your previous thread) with a 9 yr old and you did not invite her for a meal, you simply invited her daughter for a playdate - what was she doing there until 7 o'clock!
I saw your other thread.... don't worry. She's bloody lucky you entertained her for that long cheeky cow. You don't invite yourself for the day because you don't know the parent when your child is going into yr 5 FFS, you invite the child to yours instead. Cheeky mare imo.