Sansa had reason to distrust Daenerys. The Mad King killed her uncle and grandfather, and Sansa was at the mercy of a queen while a hostage in King's Landing. However, she rebuffs the Dragon Queen even when Daenerys risks her life to defend Sansa's home against the Night King.

Why is Sansa hated?

A big portion of the hate against Sansa boils down to the fact that she is too feminine for people's tastes. Her interests are too shallow, she is only interested in learning how to be a lady and talk about being queen (which, for the record, she had been groomed to be interested in.

Is Sansa jealous of Jon Snow?

As you say, she rejects him in the beginning, but there's definitely something in her that's … it's kind of a jealousy toward Jon. He's getting all of the credit for basically Sansa saving his ass. Obviously he played a huge part in the Battle of the Bastards, but Sansa really saved him.