I am hoping your social anxieties are not rubbing off on your daughter. You mention your daughter has trouble making friends...so she needs you to help her.
You need to help facilitate ways for her to have fun and healthy relationships with friends...even at the expense of your own fears or frustrations. It is not an everyday occurrence..but needs to happen often. I understand your feelings..it disrupts your schedule and the privacy within your home...I get it.
I too am a person that loves my home to be neat and organized and peaceful. But with 3 kids, 2 boys and 1 girl ,that just ain't gonna happen...and the oldest is a drummer and plays trumet. And with a drummer...the band usually will meet at your house cuz they are so dang difficult to transport. Sooo there goes my peace and quiet. But...it is about him and not me! He has talent and a love for music so I do all I can to help nurture that. We host the band weekly and I make a buttload of snacks for them. During the summer we open our yard weekly for family swim time. Does it get messy? Yep. But at one point I tell everyone to help clean up and they are not allowed in the house.
I also have a weekly homework group for my oldest's friends and my daughter invites a friend or two. Sooo, we have about 10 kids scattered around the house working on homework, laughing and talking. And...I keep the snack table full. Do I REALLY want this brood in my home? Not particularly but it is fun. Would I much rather enjoy some peace and quiet?? Heck yes! But again..this is about them and not me. I see the current and future importance of having strong bonds of friends to help and support my kids once they hit those teen years/High School years.
I am hoping these activities make for good, solid friendships with both genders. That is why I disrupt MY life for these loud and messy activities. And, I would rather have them in my home than anywhere else.
This also opens myself up to meeting new people my age and I have made some great "mom" friends.
I understand your house is small. Try scheduling activities like the friend coming over to make cookies or a dessert, or make a craft and have hot chocolate. Have a reason for the playdate and not just random chaos around your home.
Good luck and best wishes!!