We did 2 different gyms for 4 years, one for the boys and one for DD. Its doable, although difficult. Got really challenging as kids got to higher(ish) levels (6-8). Different meet schedules, different pick up/drop off, different booster clubs, etc. Worked ok but only when I was super sure that DD needed to stay where she was - as soon as the other program got on its feet I made her switch (other reasons too - but my sanity was a big one!).
Honestly, the driving, coordinating, etc were difficult and exhausting (its just me and my elderly parents doing it all here), but what got too difficult was the team politics - HCs have had conflict and one is polite about it, one not so much - my kids were constantly feeling like they should be supporting each others teams - but that the teams/coaches disliked each other and there was back biting/rumormongering from one - never face to face with me, but DD heard tons...once my kids got to the point that they spent 16-20 hrs a day at gym, this became quite toxic for us!
In a bigger area with more choices and more specializing between gyms I think it would work better - GOOD LUCK!