I have been asking myself this question ever since I completed the civil war quest line for the Stormcloaks. I mean, being the widow of the High King of Skyrim who was killed by Ulfric Stormcloak, Leader Of The Stormcloak rebellion and Jarl Of Windhelm would make you despise the dude a lot more than any other Imperialists. Yet she politely agrees to stay in her position of Jarl and act like her husband never got obliterated by Ulfric. Sure, sure, I know Ulfric never took the High King's throne but c'mon now, if she was that patriotic of her views which support the Empire she would at least do something to show she is disappointed by the Stormcloaks taking Skyrim or just something at least.

She does it because she knows she has a responsibility to the people of Solitude. Plus given Ulfric's other choices for Jarls I would shudder at the thought of who he'd place at the seat of Solitude.

I'm certain that Elisif is most concerned about what is best for the citizens of Haafinger (Solitude). Staying on as jarl would be oodles better for them than having some Stormcloak appointee sitting on the throne, acting like the Great Conqueror that keeps punishing the citizens for having supported the "wrong side" in the civil war. For them, she is willing to suppress her displeasure and focus on the job at hand.

Yeah, it's important to note that, naive as she may be, Elisif looks to her people first. She almost sends out a regiment to investigate some people who 'MAY' have disappeared in a cave. It was a very 'My people need me!' moment, luckily tempered by Falk's recognition that there's kind of a war on. She sides with the Empire because she legitimately thinks it's best for her people, but she's not going to stick her neck out after Ulfric takes over, and have the axe fall on the citizens of her hold.

Like in Whiterun.

By bending knee to her husband's murderer when left with no better option for Haafingar, Elisif has shown that she can do what Ulfric cannot: swallow her pride.

I really think that Elisif is one of the more interesting, if woefully under developed characters in Skyrim. If she had gotten half the development as Ulfric or Balgruf (both of whom still need more than they got) she would easily have been one of the best characters in the series.