I replaced my kitchen sink faucet for the first time today. It seemed like all was going well until I noticed the old hot and cold hoses now didn’t reach the new faucet. Are there extensions for these? Is that common to happen or have I maybe done something wrong?

Im installing a new kitchen faucet. I have disconnected all hoses and the sprayer from the kitchen sink. I have disconnected the handles and stem.

My problem is Im not sure how to remove the two washers directly under the sink handles for cold and hot. Once I get them off I should be able to remove the remaining locking nut on each side.

Any suggestions to get these rusted pesky washers off?

I have the following tools at my disposal:
Basin Wrench
Pliers
Screwdrivers
Drill
Dremel Rotary Tool
Small Chisel
Hammer
Mallet (Metal and rubber)
plus pretty much any other basic tools.

Any help much appreciated.
Oh yeah, I meant to say the washers are in the cabinet area of sink, directly under the handles. I believe it’s considered a bottom mount faucet.

Its just a white plactic cylinder, about an inch and a half in diameter, about 2 and a half inches tall and it has a removable chrome cover that matches the rest of the fixture and it just sits there on the faucet fixture to the far right, along with the spray hose and kitchen faucet. The chrome cover has a small rectangular hole in it. The faucet already has a spray hose, so I’m guessing this is just a missing tool or something, like maybe a water dispenser? Looking under the sink, though, it looks like there are two hoses meet at the bottom of this apparatus, one going to the dishwasher and one going to the disposal. The reason I’m writing and the reason this is such a drag is because every time the dishwasher empties, the water, at least some of it, travel up to this thing and leaks all over the kitchen counter. It doesn’t appear as though the hose connections were rigged in any way, that it is meant to be this way, but that, if that apparatus at the top of the sink were not broken, it would not leak, but it does. I need to find some way to either fix whats on top of the sink or plug it up, but I dont know what it is. A logical solution would be to bypass it, to take the two hoses that meet there and hook them together and bypass the thing all together. there’s a problem with that though, 1.) they are diff hoses. the one coming from the disposal is black hose typical stuff and the hose coming out of the d/w is that much smaller, hard white reinforced hose. I have NO idea how to connect these two. I have pics of this apparatus if you’re willing to look at them.
Actually, I think I found something. This is the set up I have

http://www.terrylove.com/forums/showthread.php?26836-Water-comes-up-other-sink-when-disposal-is-on

The "bone heads" that installed the waterline to my trailer put the main shut off valve 4 feet down a plastic pipe. Some special tool is needed to shut the thing off? Short of digging up the ground 4 feet around the pipe, is there anyway to turn the water off at my faucet so I can replace my kitchen sink faucet? Can I crimp the hoses somehow???

Our kitchen faucet inexplicably got holes in it and water was leaking or spraying out. I got to the end of the steps when I had to connect the supply lines and the supply lines were too small. Can I fix this with rubber connector hoses and ring fasteners? If not, what would you recommend?