Funny, I was just rewatching that part.

I'd say his biggest problem is not with what she did but how: keeping him in the dark and secretly working to undermine him. They're supposed to be partners and co-ordinate their actions. Claire deliberately breached the trust between them to remind Frank of her importance, as she felt he was not treating her as equal.

Frank also wants to distance himself from Remy Danton, whose money comes with lots of strings attached. Remy used to be his press secretary and presumably knows where all the bodies are buried. The thought that this knowledge could be used against him makes Frank uneasy.

Besides, he was under a lot of pressure when he took SanCorp money before and spent it to fund the library in his name at the Sentinel, with the understanding that he will be able to reciprocate once appointed Secretary of State, and then found himself unable to deliver. He needs SanCorp to buy political influence but wouldn't want to find himself in this position again.

Claire's pet project, the Clear Water Initiative, is just a front for pay-to-play money: were Frank to find himself out of power or with his influence diminished, all the donations to it would quickly vanish and it would fold. Thus, what he tells Claire is objectively correct, however this is not what his ambitious wife wants to hear.

As for Peter Russo, the original plan was to have him installed as governor. With no political power base of his own, and his compromising past that could be easily used to blackmail him, he would be a puppet in Frank's hands. (At some point Frank utters that "power is the people you collect" or something to that effect.)

Things only change after Russo threatens to expose his role in the takedown of Michael Kern, the Secretary of State nominee that Frank had discredited. At this point, Frank realizes that Russo won't be easily controlled, and comes up with the alternate plan to get rid of Matthews from the White House, freeing the VP seat for himself, turning what seemed like a setback into an even better opportunity. Only at this point does he decide that Russo has served his purpose and needs to be neutralized.

The dynamic between Claire SanCorp and Underwood is fairly self evident.

The timeline of Russo's threat to expose Michael Kern events was a little confusing. It happened after the wife betrayal and because of failure to get the water shed bill passed.

The show seems to strongly hint that getting rid of Russo after using him was the plan all along, and Underwood always had his eyes on the VP seat. He says something along the lines of we are done using Russo and now we should try to move him to the sideline.

I'm not sure if there is sufficient evidence to prove that Underwood's original plan was not to get the VP seat. Although how exactly he would get VP if Russo had won is still a mystery to me. If he always wanted Russo to go away sometime during his plans then I don't see his wife's collusion and betrayal as a major impediment to his plans.

Maybe Underwood was so upset because the failure to get Russo elected lessened Underwood in the eyes of the President and made the VP position harder to obtain.

I see it differently. Peter Russo wasn't being set up to fail from the beginning. It was just one of the possible outcomes Frank foresaw ("Who else is from Pennsylvania?"). Russo only sealed his fate by being unable to handle the pressure (while interrogated about his past), turning against Frank and threatening him.

And I don't think Frank wanted the Vice Presidency either, he just availed himself of the opportunity that emerged due to the chasm between President Walker and Vice President Matthews.

Frank is after raw power, and doesn't mind (or perhaps even prefers) being out of the spotlight. He could have easily become the Majority Leader himself but would rather remain as the much less prestigious Whip because this is how he can wield real power behind the scenes without being exposed: he can make his political maneuvering appear as the actions of numerous other people in the public eye, only taking credit himself when he wants it (the Education Bill).

The VP is a largely ceremonial position (unless the President is incapacitated), and the public exposure it comes with makes it impossible to stay out of the limelight, which is hardly Frank's preferred arrangement. However, it offers him the opportunity to exact revenge on the people who reneged on their promises to him by working to undermine them from within, and to further his power base, which makes it worthwhile, particularly as he assumes he can concurrently retain his influence as the Whip through a successor of his choice.

I believe Frank's general aim was to make the President estranged from his staff and unsure whom to trust, and all he needed for that was access to President's ear, not necessarily becoming a part of his administration. The Vice Presidency is just means to an end but he could have achieved the same differently as well.

That's a fair interpretation, there isn't enough evidence to falsify the interpretation. The weird chronology of events is a little confusing to me. I might go back and rewatch it at some point to wrap my mind around the chronology. I'm not upset by your interpretation.

I just wish that the show would make it a little more clear what Underwood's original plan was. He would have a puppet governor and then what? What was his original next step? (assuming betrayal hadn't taken place)

I think Frank's planning went like that:

1. It's well worth it for him to insert himself into the candidate selection process to build up his influence and reputation with the President, while making sure others don't get the chance to do so.

2. When he realizes Russo is technically being considered as a candidate, offer his support to compensate him for the shipyard closure, or at least pretend to do so, as it doesn't cost him much to do so even if nothing comes out of it.

3. If something does come out of it, then Pennsylvania is a perpetual swing state. He could perhaps use his influence over the governor to try to sabotage Walker's re-election in 2016, and prepare the stage for his run in 2020. It is also an important area of business for SanCorp, so he might be able to solicit more donations from them, and it gives him leverage over the company should they become problematic (through Remy).

4. Lots of other not immediately obvious opportunities too, it definitely helps to have this kind of influence, although I think the immediate plan was to get closer to President Walker and make himself indispensable.

In the end, I guess we can't be sure what Frank's original plan was, it's left open to our interpretation. In S1E13, which I've just watched again, Zoe, Janine and Lucas also seem to suggest Russo was being set up to fail from the start. Your version is certainly corroborated by a lot of events.