I don't have any ideas for garden themes, but the technique I see most often for keeping flowers under control is to use a custom design on the ground. If you make one of your custom design slots a transparent tile, you can place the "design" around any flower areas and it will prevent flowers growing in those spaces. I prefer just trying (unsuccessfully) to dig up my flowers before they get out of control, but I've seen people use the transparent tile technique a lot.
As for moving flowers, I don't think there's an easy way to move them around the island. If you want to get rid of them, the fastest way is to carry around a trashcan, fill your pockets with flowers, throw them away in the trashcan, and then keep going. You won't be able to get the flowers back though, so it's only good for destroying them completely!