And I personally think Kershner did direct the best one, in terms of drama and characters. The humor I don't think is inappropriate at all--its character humor. Lucas would go for jokes or slapstick but Kasdan and Kershner are more into humor that comes from characters and their relationships. One of the best examples is 3P0 telling Han he'll have to replace a part, Han yelling at him to shut up, and then quietly relaying the same information to Chewie. Its not a joke but its funny, and it comes from the eccentricities and personalities of the characters.
FYI the malfunctioning hyperdrive was something Lucas added himself. Aside from "I am your father" and Han-frozen-in-carbonite, one of the main tonal changes Lucas made from Brackett's first draft was humor and slapstick, namely the ongoing gag of the hyperdrive breaking and 3P0 never quite put back together. Kasdan and Kershner made this centered around the characters of course through the way everyone reacts-- ie "would it help if i got out and pushed?" "it might!". Kasdan and Kershner's humor is more subtle and based on character dynamics, while Lucas' is more gag and slapstick based.
I don't think Kershner and Lucas hated each other--the animosity between them post-release is way overblown--but at the time of course there was massive tension. Kershner was justified in some sense because his ideas were usually bettter--and ultimately the ones that ended up in the film--but Lucas' hostility was also justified in that Kershner went way over budget and schedule. And thank god he did. If Lucas had his way the film would have half the budget, would have an erratic pace of only 100 minutes and would jetison most of the wonderful character moments and supulchral tone that the film is defined by. Seriously, that was how Lucas wanted the film to be made but Kershner and Kasdan wouldn't let him and Kurtz let them both get away with it.
I don't think he is jealous--in fact, all indication is that he considers it a lesser movie because its not the way he would have done it. I also don't think he's that resentful, and neither is Kershner--true, Kershner didn't want to work with Lucas again and Lucas didn't want to work with Kershner again (Kershner said he wouldnt direct ROTJ and Lucas never asked him) but at the end of the day they made amends and Kershner even visited Lucas on the set of ROTJ. I think there is still a bit of unspoken tension but I don't think its as scandalous as some people make it.