Rancher...can you get a rope on it and pull it towards the tree I see behind it? You will need another person to work the rope. It's hard to tell how close to the back of the coop it is.
I had a guy here a few weeks ago with a little tiny excavator. A huge tree fell from across the creek and my neighbor cut it from the other side. Just saying because he grabbed the tree where it was down a 30 foot bank and pulled the whole thing up and out with the claw on the bucket he was excavating with. (I'm working on building a horse barn and he was helping me set the posts.) Maybe you can find someone close by who has a little machine like that to grab it and pull it over away from the coop.
I take some better pictures. I'm not sure a machine can get in there because it's so soft. It looks level and all that but there are ruts from where a truck must have gotten in and not to far. I mainly mow it because it helps someone what to keep thing dryer.
Too we don't have the money and at this time aren't sure how much longer we'll be here. Some days I think it's time to give up and move into an apartment. Maintaining a house is not easy when you're retired and not in good health.