Get a steel-string acoustic, with something like .12 or .13 string set. Play that for a while every day, and an electric will feel like feathers after that. Seriously, it'll really teach you to press just the right spots only and train your finger strength the best.
Also, try other type necks and playing positions. A very thin neck is a real pain to chord on very quickly, and a V neck or a properly thick one is WAY more comfortable for chording, because the neck gives the palm support it needs for leverage over strings, which a thin one doesn't.
Furthermore, if you play mostly sitting, it could just be that you approach the neck too directly from below, which also means that you have to apply a lot of pressure towards your body from the elbow onward - if you keep the neck much lower like when standing, you're forced to approach the neck with wrist more like 90 degrees to neck, giving a good gripping leverage naturally (your thumb becomes a hook that serves as a good pivot point).
I guess everybody gets tired with barre chording too much. Often it can be helped by substituting every second or third chord with an open equivalent. I also hate playing songs that are all barres...I never make them that way, but I have a few songs that have all-barre verses for instance, and when we play the song a few times, it becomes clear that I'l quite looking forward to getting to the chorus so I can just drop a proper open chord and rest my hand for a while
Likely it's a combination of all kinds of things. No way but play differently, different guitars, and it'll get there. I remember how for the first time I learned a full barre chord it took me a week before I even begun to think it possible I could ever learn to play the sucker properly, and years to get used to using them more than just now and then without tiring my hand.
p.s. I now have been trying to learn a few things on piano, just basic chords, and my right hand feels incredibly tired after just a while of hitting them...