I just dont think that they liked each other very much. But they were almost "forced" inot an acquaintanace because tehy were teh same age and Highbury is a veyr small town. I dont see them being close friends during Jan'es visits during her childhood and teens .. Jane is too serious and a little dull IMO. Emma while less accomplished is a lively person... and more "fun". However while I dont see that Emma realy ever "snubbed" Jane or that as kids one of htem had to be brought home howling from a kids party becuase of a squabble, they just didn't IMO hit it off and weren't compatabile. I dont think that tehy will be that much friendlier now tahat htey are older and married..
but that does not excuse Emma's slowness to "do the righgt thing" by Jane when she does visit. Jane may not be a fun compnaion, she may not like Emma particularly but she's a distressed gentlewoman of the same age, who has a very dreary future ahead of her... Emma SHOULD make more of an effort with her, inviting her to Hartfield without Miss B at times and letting her play the piano etc. It would be tedious problaby but not as tedious IMO as having to vist Miss Bates frequently. So she raelly shoudl have done it and perhaps she adn Jane woudl have then gotten on a bit better. Tehy dont have to be best friends, just to be agreeable with each other...