In the end, you have to do what works for you, your pen setup, the disposition of the cattle you happen to have, etc. Your best tool is careful observation of their behaviour... you are well along the way to that. I can tell because I very well understand and relate to and have seen the exact same behaviour in cattle over the years.
Comment... have you ever driven by a dairy and seen a long line of cows waiting to go into the milk shed? They HAVE become COMPLETELY trained because they are fed twice a day, have been at the dairy for several years and the dairy herd is almost completely stable... add or lose a few cows at a time... no mass movements (typically). The cows come in, without being called, twice daily, at the same time, and line up, in the same pecking order, every time, just like school children. typically a small dairy will have maybe 10 milking machines and thus let in about 10 animals at a time where they are both milked and fed. Then that group is let out and the next 10 come in. they even go to the same milking stand each time. Many things at play here, that pattern the animals for maximum convience of their handling.
You can do the same... but not likely since you will have more turnover, etc. etc.
You are experiencing something that I commented on in one of the very first posts... sufficient feed bunk space is necessary else competition causes problems. I recognize the animal between the bunk and the fence problem... that is simply what happens when the bunk is in proximity with the fence.
Now, I agree that your idea is fully formed and should be tried. That is, capture the first group that comes in and feed them (sounds like they come when they sight you without calling), then move to the next group (likely they will begin coming before you call when the see the first group move into the pen. Initially, I would feed the first group and turn them out into a different pasture or holding pen before letting the next group in. It's kinda hard to make suggestions, not knowing exactly your pen setup, etc.
It's possible that you can pattern each animal to go into it's "assigned pen" but I don't think that is going to happen...at least not with a clean cut. Your best bet is to seek to capture one group first, then the next group.
Then, when you let your horns go, let the exit be the pen/chute setup you wish to pattern them with... When the group is completely finished eating, I'd just open the pen/chute/gate and let your super smart lead cow of gold lead the group out... likely they will all find their way out easily playing follow the leader... it is possible that the first time you may wish to insure success by hand feeding/encouraging your lead cow to follow you while you back out thru the pen/chute/gate setup.... when they start following thru, I'd circle back around to the pen and provide gentle pressure on the shy ones such that they keep observing the individual animals following each other out and it becomes their idea to follow as well.
Yes, a wire fence will keep the two groups apart.... assuming any strength/visibility to the fence at all... remember, once I commented on the effectiveness of a visual barrier.
I believe that electricity would be your friend in reinforcing this fence... you could put up a few strands of hi tensile wire and reinforce it with an electric fence charger.... hot side toward the mean group of cattle... they will QUICKLY learn that they must stay away from that fence or get bit. Net is that the construction materials of the dividing fence will depend on the usual variables... time to build fence, $$, skills in fence building, materials available, length of time you wish to use that fence and the amount of pressure you wish the fence to ABSOLUTELY withstand.
On the low end... I believe a single strand of electric fence wire would do the trick.... put the mean group in their pen, let them complete eating, put out feed in the other side of the pen, let animals test the wire numerous times until they get the message, then let your horns in to eat and make the mean group envious. At the other end of the fence spectrum is a pipe fence that will withstand a stampeed of animals hitting it and be 7' tall preventing anything from jumping over. A reasonable, in-between, reusable fence materials structure is to use T posts and 16' cattle pannels for the fence. I have done this to try out a fence/pen layout, then later removed the posts and cattle panels when different needs arose. The T posts and cattle panels (panels are kinda expensive, I grant) can be reused later as needed, or that pen can serve very well, assuming not too much physical pressure or jumping cattle, for many years.