Not sure if removing the stock music app is smart, but if you WANT to, you have to be rooted, go to system/app and remove music.apk
HOWEVER, I had the same problem at one point and found out that last.fm was causing it. It was a bug in one of their updates that when it scrobbled the music it would skip to the next track. Not sure if they fixed it but I have since switched. Food for thought.
I'd just stick with an alternative music player, PowerAMP has an amazing EQ and even though it says it's just a trial, all it does when that expires (so far) is bug you to buy it but nothing is limited in it. The trial is about 2 weeks I think too.