I am trying to understand how all of this got so jumbled. You invited this girl over to play with your DAUGHTER.
This was to help the mom, who has just had a baby. Awesome!..
The kids played on the slip and slide but the guest got tired of that and suggested they go to her house.
I can understand that if there was just 1 thing to play with they would get bored. You said you made other suggestions, but next time you need to have some set activities. Or think outside of the box. Include your daughter in this plan.. Let her know that her friend will be there for 2 hours, 3 hours.. whatever.. and make the plan..
Also you must speak with the kids about how to host a guest in your home and how to behave at other peoples homes. This is not a last minute conversation. This is a conversation over time in small talks.
Slip and slide, swings, sprinkler, baking cookies, girls playing in your daughters room,Playing store, Setup their own water obstacle course. or very last resort.. a video, karaoke.. Kids are clever..
Maybe you could have taken them to the park to play.. Just call the mom and say, the kids are finished with the slip and slide, would it be ok if I took your daughter to the park with my kids?
Then pack up some snacks and load them in the car and let them play at the park.
Also remember, your son is not really part of the play date. This was for the 2 girls. He maybe needed to have his own friend over, but ONLY if he is good at playing well with others. Or you would need to keep him occupied and busy with you. Just because the guest was tired of the slip and slide, does not mean your son could not continue with you watching him.
These girls do not need a little brother to play together.
And No, If the plan was to give the mom a break, I would have never considered taking all of the kids over to their home, even though the mom was being gracious.
If I was completely desperate I would consider taking the kids to play at a playscape associated with a restaurant. It does not have to be McD's.. I am sure there are other places they could have played. Here in our city there are locally owned food places, that serve family friendly foods, but with a play area. Ice cream, finger foods, whatever I would have contacted the mom and packed them up, purchased an ice cream for each and let them play.. Again you supervise brother, so the girls can play together.
Do not beat yourself up. Take this as a learning moment. At some point call the other mom and apologize and let her know you would love a do over, but this time have a plan.
We live in the smallest, least glamorous home of all of our daughters friends. That never was an issue. We do not waste time comparing our lifestyle with others, instead we just love people and sharing our fun with them.