the concepts of play and fighting

This excerpt is from For the Children's Sake by Susan Schaeffer Macaulay. It encapsulates my philosophy of life and learning pretty well. I intentionally give my children large blocks of unstructured time, space to roam, and freedoms to do just about anything as long as it doesn't impinge on others' person or property. While it sounds good theoretically, I am struggling to make it work for me and my family. 

I am with my children all of the time. I am physically present all of the time. I am mentally and emotionally available to them probably sixty percent of the time. I have done everything I know to do to live this philosophy. 

And yet, it seems like my kiddos can't think of anything to do when I want them to. If we have friends over, they will disappear for hours, barely turning up to eat. 

If it's just us though, they want to sit right next to me, or on me, or fight about who is going to be on me. Or they'll come in the living room where I am obviously otherwise occupied and start noisily eating something which one-grosses me out, because I hate the sound of people chewing and eating and two- isn't allowed in the living room, or just start asking me inane questions or fighting and bickering, trying to get my attention. 

I spend a few hours with them in the morning, reading out loud, talking with them, doing schoolish type things. By then I need a break. I need space for my body where no one is touching me and space for my brain where no one is asking me rapid fire questions, or demanding I do something for them. Or whining!!

Then it seems like I spend the rest of the day fighting for a break and fighting to get them to help clean up after themselves, and help one another and me, and fighting to get them to stop fighting! I'm struggling. 

How much time should I be "all there" ? How much rich creative play can I really expect? Why do the books say boredom is a good thing as it launches creativity, but in practice all they can think of to do is torment a sibling? Why do they need to make their noise and mess right where I am? Why don't my children stick to the boundaries? They matter more than the furniture but it still drives me nuts that the carpets and couches are stained from the eating in the rooms they're not supposed to and there are holes in the upholstery from scissors and saws and "exploration". I GIVE them interested support and empathy during their quarrels and try to really listen and reflect their feelings and they still demand more.  

How do children learn to play without my intervention? Or when they just don't want to? How do they learn to get along without making me crazy? How I stop taking their big emotions onto myself? 

I'm struggling with these concepts of play and fighting. Struggling.