A Civil War?

[Voralphion]

Imrahil was teh prince of Dol Amroth and had a legitiment call to the throne of gondor,

I don't think he did. I don't believe he was descended from Elendil, either through Isildur or Anarion/Melendil and so would not have had a claim to the throne of Gondor, or the Princes of Dol Amroth would probably made a claim long before.
I don't think the prospect of the people following Faramir is as clear cut as stated. The people were thrilled at the prospect of having a king as soon as Aragorn had arrived and healed the people in the houses of healing. The people wanted a king to return, and bring back Gondor's glory days, so it is possible they would have accepted anyone with a legitimate claim.
If a civil war did break out however and Rohan did intervene on one side, it would have been to support Aragorn. Eomer had a strong friendship with Aragorn and probably woul have supported him. I don't think the prospect of Faramirs relationship with Eowyn would have been a factor, because if Faramir was as power hungry as he would have to have been to start a civil war, I don't think he could have won over Eowyn.

[Boromir88]

Tuor I like the scenario you have brought up, with the whole what would Eomer do? I happen to agree with Voralphion, that Eowyn wouldn't have fallen for Faramir if he was "power hungry." However, you can't help but think, hey maybe this is Eowyn's chance to get back at Aragorn, that is if a Civil War started. But, I don't see Eowyn as a revengeful type. And without the relationship between Faramir and Eowyn, Eomer would definately side with Aragorn.

Also, Lachwen, thankyou for the correction, if I say something wrong I would expect to be corrected.