I prepare the mulberry bark by scraping it off the pruned branches, soaking overnight, and gently pounding with a rawhide mallet. It's basically the first three steps for making mulberry paper, but it leaves the inner bark as longer fibers. The result is really more twine than yarn but I plan to try blending it with reclaimed silk fiber from shredding thrift-store silk shirts for a softer result. I'm also saving thistle stalks from my yard to try retting for their fiber, just like flax but more prickly.
Easter egg grass is an interesting spinning fiber, isn't it? I also found some thinner plastic/Mylar shreds with the gift basket wrap, and it blends with other fibers even better. Eventually it'll make its way into a nice sparkly carded batt, after I finish carding up this Suffolk fleece from the 4-H kids. Do you have 4-H where you are? They gave me this five-pound fleece for helping with their booth at a local festival.
Of course, if you do shave your dog...it's summer, it's to keep the dog cool!