Is having two separate coaches going to be counter-productive?
In my honest opinion and experience, very counter-productive.
I am concerned though that having a second instructor may be
counter-productive. There's a huge chance that a new coach will have a
different coaching style, different ideas about optimum swings,
stance, etc. and lessons here could antagonise the teachings of my
I have never had a golf coach. However, I have watched golf, instructional videos, and had multiple golfers/golf pros/etc. give me advice. Most of the time, philosophies on how to approach the fundamentals of the game varied, sometimes greatly.
For example, two golfers may instruct you to keep your lead arm straight through impact, then follow through...but one golfer's philosophy may be to have even weight with your head behind the ball at impact (a flatter swing) while the other golfer's philosophy may be to have most of your weight on your lead foot with your head over the ball at impact (stack and tilt, a more upright swing). Same fundamental, different philosophy.
I'd imagine the philosophy between two coaches would be different. Even if one coach is a "protege" of a more established coach, there will be slight differences in philosophy.
Because of the mental aspect of the game, I would suggest that you stick with your current swing coach, as your game is coming along nicely, and you have been working with his philosophy. Next time you see your coach, ask about fundamentals that you can work on while you are away. Thus, you will remain to have one philosophy that you follow.
Some pro golfers meet with their coaches 3-4 times a year to go over fundamentals and philosophies. Some of us are more involved. Some of us are not. Once again, the kind of golfer you are comes down to the philosophy you follow. Adding another coach most likely means adding another philosophy which most likely means the mental aspect of your game will suffer.
Personally, I have tried many golf swings and philosophies, but through time and frustration, I decided to work with what I naturally have (for example, even if I am cognizant of shortening my swing, I still swing my club past parallel with my woods and long irons during my backswing) and work on fundamentals. Also, I limited my thoughts before my swing to one swing thought. After deciding to let go of my mental struggles and frustration, my time on the course has been more fun and I have been playing better. It's nice to hit drives around 300 yards and hit the fairway half the time...still have the short game to work on...
I know this would be a good question for my current coach but I'm not in contact with him whilst I'm away.
I would be weary of bias ;)