Those look VERY much like two feet to me. When I worked on an archaeological dig in AZ, there were hundreds of Native American petroglyphs and most of them were feet like this. It was at a place that was a resting place for travelers and the petroglyphs of feet were drawn by people on a journey. I don't know if that is exactly what your ring might represent, and I have no idea about the umbrella symbol, but it might be a starting point for further research.
Compare the criss-crossing sandal straps on the feet in these petroglyphs to the lines on the feet on your ring. I'm going to go out on a limb and say I would bet this is a ring is Native American and that it is a traditional design, intended for travelers. (But I'm not an expert and could be way off)
The petrogylphs in the photograph were drawn about 800 years ago and I am guessing that the design motif has been in use for centuries.
Here is a photo from the dig: