As a paladin player i know what you are talking about , I do feel the same when i found the way Lay hands work, yet its as you mentioned one of those hard coded feature that NWN has, basically the features of class and how they work are all as that. There is no way to change the hardcoded part of the classes sadly. yet i can say too that eventually lay hands become a very useful feature now that you start to hit the high levels, getting to get a lot of healing in the mean time you have to move away from a heavy combat and return almost as new one round later is a good thing, I say this by experience
See the paladin warhorse seems to be an addition to the Layonara paladin, compared to the regular game which doesn't get a war horse.
If you increased lay of hands to one use/2 lvls...it would become quite powerful. This I say not only for healing, but also against killing undead. I think it deals out damage equal to your cha mod x level. Might be out of balance to increase its usage.
You get the paladin mount at level 14!?! Why such a high level? If you get it at level 14 that warhorse better be a really powerful companion because that is a bit ridiculously high accounting for the extremely slow leveling in Layo which is another thing that I don't quite understand because the game world is very low level unfriendly.
Well we must take in acount that the Paladin warhorse was added after the relase of 1.69 patch, as for why so high level. Well there are people I am sure that could answer better than me on this one yet I am going to give my thoughts anyway .
The last suggestion (a feat allowing additional uses) may be possible (a cursory look at feats.2da doesn't suggest that it is not) but non-trivial.