Thats one pimping looking RV already there dude, love the material!
That area in under the seat should be more than capable of housing the computer and other parts, but I would consider dividing the space into two parts, and housing the amp in a second enclosure in there, to minimise heat pollution between the two components. Some amps generate a fair bit of heat, but can be kept cool enough with just some convective air currents, but you don't really want that heat spreading into a computer that you want to keep as cool as possible.
For the speakers, I guess it depends on a couple of things, the budget you have in mind, and the sound quality you want to get. You could try fitting better quality speakers into the current positions, or mounting into a speaker box kind of arrangement. You could also try your idea of home style hifi speakers, one positive with that would be that you can have nice tiny satellite speakers, then just one reasonable size sub for the bass and midrange. However, I would try that with a borrowed set inside the RV to see how well it sounds. You would also need to get it running off 12V, rather than the 120V or 240V mains current it would be expecting.
If its an RV, it might be worth checking out a small size generator too, like the small Honda units. They are 4 stroke, and quiet as, so its the kind of thing you could just drop on the ground outside the van and run if you want to keep sucking down the volts inside the RV with the computer and other gear. Can also use it to keep the battery topped up if you are going to be there for extended lengths of time.
For the screens, why not go for 2? Have a 7" touchscreen in the dash for when you are driving, then put a 19 odd inch screen in the back to use as a TV, media player, dvd player, and general use PC.
Maybe one thing to consider is having two PC's, one for the dash to use while driving, and have it just for music and nav, then have a higher specced machine in the back of the RV for use while parked up? Hell, if you had the budget, you could even look into a reasonable PC running Windows Media Centre or the like, with a 32" or 37" or even 42" LCD on one of the walls.
Go Nuts!!! But either way, post pics!!!