After seeing the importance for your logo to stitch well, this is the design idea that I came up with. It is a clean and bold logo, which will sew great on caps and other apparel. The colors are pretty straight forward, but can be changed easily as needed: green and sand (fairways and traps).
I deal with digitizing and embroidery on a daily basis, so it is important to keep thick lines where possible and to keep things as simple as possible. I look forward to hearing your thoughts on this. Thanks!