Head WAY down when cantering

I ride my 21-yr old Western Paso Fino gelding on my property, and his miniature mare 'girlfriend' is inseparable from him. Arthur (the gelding) will completely freak out if Lulu's (the mare) over by the stallion's or the other gelding's stall.
So whenever I ride Arthur, Lulu has to tag along, and she just runs around us while we ride. Naturally, being the pain that she is, she has to buck at Arthur when we try to pass her up. Arthur, assuming alpha over her, pins his ears, arches his neck, and sometimes tries to buck back at her.
When I canter Arthur, Lulu runs next to us, and Arthur usually tries to tuck his head way under himself. When he does this, the canter gets rockier. He's gaited, so his canter is always smooth, but when he tucks his head under himself the canter gets a lot more like a rocking horse. He seems to be leaning way forward and way back in the canter when he tucks in and lowers his head like this.
I always pull his head back up when he does this, because usually it leads to bucking at Lulu.

So my question is this: Should I let him keep his head down when we canter, or pull it back up? Is there a 'correct' way for a Western horse to carry his head in the canter? Thanks,

Equiniphile

depends on what you mean by tuck his head down. it could be subtle or he could be behind the verticle and leaning.

First of all, I think that your horses need learn how to be separated for "work time" as opposed to "play time". As your "working" situation is currently, you are encouraging the horse you are "working" to entirely ignore you and go off bucking with his friend.
As far as I am concerned, the horse has 23 hours a day to run around and do what they would like - they can give you an hour of their time.
I think once you fix that - your riding sessions will get worse before they get better but eventually he will learn that he is going to see her again and he can focus solely on you for a while.