You have been given some great advice and things to try.
I think in the end it does just come down to practice. I remember when first starting out that it was so frustrating to me that I couldn't outline a cookie without the icing line breaking, falling off the edge of the cookie, etc. It looks so easy when you watch other people do it, but it takes quite a while to master.
Don't give up, I am sure your cookies look great and you will be surprised at how your skill improves as you keep practicing.
One thing regarding tips and bags, I find that tips, especially PME tips, give me the best results. I've been experimenting going tipless with master piping bags, but I don't like the results I am getting. I am going to keep practicing, but it just goes to show that there are many different ways to ice a cookie and some are going to work better for some people.
Good luck!