Yeah, Cheney has more influence over the president than any other veep in the past ever has, so there'd be plenty of ways to yank him out as well if you really wanted to.
As for Pelosi, don't gimme that shit. If you remember correctly, Dennis Hastert had a jet for his entire tenure as Speaker. However, Fat Denny only had to fly to Illinois, whereas Pelosi would have to make a trip almost three times that distance, a trip which Denny's plane couldn't make in one go. All that Pelosi's aides requested was that she have a plane that could make it without stopping for fuel. And I don't know if you know anything about air travel, but public access airlines (or plane fueling stations for that matter) aren't available around the clock. Do you think that she can afford to waste any time as Speaker of the House working five days out of seven and spending eight hours on the two days she has off to make the trip there or back? If she needs a bigger jet, she oughtta get one, forsooth.
Also, the United states takes in over a trillion dollars in tax money every year. A few hundred thousand for a jet won't put even a tiny dent in your healthcare, rocko. What will is a fucking war in the middle east. No matter how much money she has to use, she would use it where it's needed, which is one of the things that matters most in a president.
As for power, try running for president of the United States while not wanting any responsibility for the position. Tell me how it works out.