We have Friday afternoons set aside as playtime with the cousins, but it doesn't necessarily happen every Friday (if someone is sick, out of town, doing something as a family instead, etc.) it's a no go. We've found this to be enough for our dc, but we have 3 dc that consider each other their best friends. For those with an only child, I can see how more time may be needed.
I had a similar problem the last few years, though it was not with friends. My problem was the phone. My family (including my dh, my dear sisters, mother, father, mother-in-law, aunt, sister-in-laws, friends, etc.) would call in the mornings during my homeschooling time. I would think I could quickly answer the phone and get back to teaching. You can see by the sheer amount of people I'm talking about here that this wasn't a good idea and resulted in me being short with the kids, feeling stressed, etc. So, at the beginning of this year, I kindly told all of them (with the exception of my dh) that I would not be answering the phone in the morning because we needed to be homeschooling and it was causing too many interruptions. For the most part, everyone handled it fairly well. It didn't stop all of them from calling, and sometimes a few disgruntled people would leave messages to the effect "I know you're in there but I guess you're too busy to talk... I just needed this one thing quickly". I sometimes have caved in and answered only to really regret it because it added stress to the day that just wasn't necessary. For example, a few days ago, someone wanted my help editing a Christmas letter. I made myself not pick up the phone, finished school, and called her back in the afternoon. Turns out that worked out fine anyway - the letter still hasn't been sent. We're just all too used to being able to reach a person immediately, but the truth is, most of the time that immediate response is not truly needed and actually prevents us from doing what we really wanted or needed to be doing in the first place. When I stick to this, and I really have about 95% of the time the last 3 months, things go great!
I think I'd let your dd's mom know that you need to do school from ___ to ____ time each day, and that you are letting everyone know that during these times, dd and you will be unavailable to everyone with the exception of your dh. Then stick to it, and soon they'll learn to call you or stop any of the other many times of the day instead. HTH - I understand your dilemma here, but if she's a true friend, she'll be respectful of your wishes and understand that school is very important to you.
In Christ,
Julie
As the years have passed, I've become a bit more structured each year. 
