I am reenacting in 2 different units. For one I am Gunner with the Brooks Light Artillery. Whenever the cannon is not available, I am Corporal of the 5th GA.
Inf. Co. A.
As long as you keep both sides informed of what you are doing, and what your future plans are, there really shouldn't be a problem.
The only issue I can see, that you might get promoted in one unit and there is no room for your rank in the other unit.
If I would be doing 2 Artillery units, I would start out as Gunner. If one unit promotes me to Corporal it could be that the other unit does not accept this.
So you would need 2 jackets. One with and one without stripes.
Handy