Sounds like the peat moss is what could be the problem.* Once it dries out it's difficult to rewet.* I'd put down a 4" layer of compost, mix it in and plant any sunlover you like.* You could make it all roses, but the heirloom and shrub roses will do best if you can't water regularly.* If the roses that are popping up are the wild ones, I wouldn't plant those, but I would destroy them.* They are terribly invasive.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.