Playroom

I spent a lot of time working on our playroom when I first created it.  I had this vision that the kids would spend hours upon hours playing in there.  Of course, I planned to be there too (I even left a couch and our desk there for that purpose), but I thought with all the toys and activities down there, they would hardly notice if I was even there or not.

Well, after a few days of rain in which we were stuck inside, I have come to one very clear conclusion: my dreams for our playroom were simply fantasies!  (*at least the room is one of the most repinned from my entire site, so someone...or quite a few someones...appreciate it...just not my kiddos!)  My children are awful at playing, and they are especially bad at playing in the playroom (they seem to do fine outside or running through the house...anywhere that involves a lot of space to run!).  Sure they'll do a puzzle for a hot minute...or throw some play dough around the room....and they do really enjoy jumping off the slide...but in that fantasy vision of our playroom, I envisioned them mellowing out in there.  And mellowing is probably the farthest word from what is actually going on!
They are constantly fighting over whichever toy the other one discovers.  And if they're not fighting, they're getting each other completely wound up...and then someone inevitably gets hurt because they've "accidentally" tackled, pushed, or bit (Levi has a very bad new habit by the way!).  Oh, and those dreams of them hardly noticing if I was even there...um, completely, completely in left field.  I've tried to walk out and it is literally about 30 seconds before my little ducklings have followed me to see what I am doing.
Now let's be honest, part of my issue with this is that I would love a little bit of a break from entertaining my children.  But my larger issue is that I really feel like they literally don't know how to play independently...and that this is a critical life skill they should have!  I worry that in all our outings, and time with friends, and activities inside the house, they think they are supposed to be entertained every second of the day.  Plus, there are a whole bunch of toys down there that we...and others...have spent a lot of money on...that never get played with!
So now we have a new mission in this house.  We are going to learn how to play.  We are going to spend time...lots of time...in the playroom discovering all the wonderful toys and activities there are down there.  I have a hard time sitting still and not doing anything...a problem I have clearly passed on to my children...so together we are going to figure out a way to just mellow...and play...quietly, independently!
Any suggestions?