It is no question that all Hans wants are the things he never had nor was given in his life. Love could easily be one of those things. But that would be more difficult for him to get since he (like Anna, again) doesn’t know what love is.
I don’t think Hans wants to be king only because he wants to be loved. My opinion is that all he wants is to be the king he knows he can be and he thinks he should be. He wants something to belong to him and a place to belong to. He wants a kingdom to rule, to take care of, to make grow. And the reward he would get is the respect, admiration, loyalty and maybe love of its citizens. I don’t see nothing wrong with that. As for his methods… that’s other story ¬¬
Personally I think the killing of Elsa wasn’t only just for the sake of getting the throne. By killing Elsa the eternal winter would be over. One can only assume that since it was Elsa who created it all. With her gone, so would her magic. Maybe at the beginning of the movie Hans planned to marry Elsa. Things with her wouldn’t work and he saw Anna as the key to his victory. But as the movie goes on and things get more complicated, Hans is in charge. Against all odds he proves he can be a really good ruler, but if the winter doesn’t end it would be the same as being king of nothing. Everyone, even himself would end up freezing to dead. Part of the reason he wants Elsa dead is to save Arendelle.