Two layers of fabric and one of batting is no problem for an embroidery machine. Check out "quilting in the hoop" on the internet It is very popular right now for people with embroidery machines. You can float batting or fabric with your hoop. Both can be attached to stabilizer or fabric that is hooped by means of adhesive or basting.
There are lots of sites with ideas and emboridery files you can download. There are even stippling emboridery files.