Regarding the issue of hay in the garden, I find that I have to be careful not to get that. Where are you storing your hay? I store mine on a high shelf in their shed, but I have to take hay from there to a litter tray at the end of their run. If I take large handfuls, then lots of it falls onto the garden, so instead I make sure I fill a large bucket to transport it from the shed to the litter tray
I second zoobec's suggestion of covering the playhouse floor with vinyl or stable matting. The shed here has vinyl flooring (cheap offcut from a carpet shop) and so it is easy to sweep.
You'll find that you'll develop your own routine and it will all become much easier in time.