Emma was the rich, leading lady in Highbury, it was for her to set the tone for social intercourse. Jane accepted attentions from Mrs Elton -- the vicar's lady is in a way the second lady. I don't think they have much in common. mrs weston and mr Knightley offered this explanation -- chap 33 --

'"We cannot suppose that she had any great enjoyment at the Vicarage, my dear Emma -- but it is better than being always at home. Her aunt is a good creature, but, as a constant companion, must be very tiresome. We must consider what Miss Fairfax quits, before we condemn her taste for what she goes to."

"You are right Mrs. Weston," said Mr. Knightley warmly, "Miss Fairfax is as capable as any of us of forming a just opinion of Mrs. Elton. Could she have chosen with whom to associate, she would not have chosen her. But (with a reproachful smile at Emma) she receives attentions from Mrs. Elton, which nobody else pays her."'

You seem to think Jane was rude and cold to Emma. Jane was always polite, in fact one of Emma's criticisms was that Jane was too polite "wrapped in a cloak of politeness"! Jane was not forthcoming during that evening at Hartfield, which was soon after she came to Highbury agfter a long absense. There are people who need time to warm up, Emma seemed to expect Jane to be immediately open with her. Mr K thinks Jane would be a better companion because she was wewll-educated and accomplished, with Harriet, Emma meant to read more and improve Harriet and herself, but their reading seldom went beyond "the first few pages". Emma liked Harriet partly for wrong reasons -- Harriet was an artless flatterer. When Emma regretted her own idleness in not practising her piano playing and practixed vigorously for an hour and a half, Harriet came in and flattered Emma by saying Emmas's playing was already so good.