Ah plumbing.... the bane of my existence at times.
Note that in most cases when using Roto Rooter that you're paying top dollar for guaranteed service. It's a bit like taking your car to the dealership. You're defionetly going to get the issue fixed, and fixed correctly, but it's going to cost you a pretty penny. You might be able to get the same job done elsewhere but you're taking a bigger risk the further down in the price pool you go. However, there might be a shade-tree mechanic who can fix you up for almost nothing. Not to say that Roto Rooter doesn't do good work, they do, but it is almost always at a premium.
Nothing wrong with getting a quote from another plumbing company/individual.
For the task at hand, water leaking at the diameter of a penny is an absolute shitload of water. I haven't done the math but if it's leaking like you stated somebody is going to be on the hook for massive water bill. Many standard faucets don't even produce a diameter of a penny on full blast. Hopefully you meant the thickness. Any repair job is going to consist at most of replacing the internal valves and should include new o-rings. If you can find the model of your faucet online you can get an idea of what these parts cost as they are usually sold together in some kind of repair pack (including everything you should need minus tools). For replacement in a typical shower they're going to have to destroy part of the wall to replace the faucet, and if it is a variety of situations the wall destroyed might end up being one of the shower walls, which would then need to be replaced. Long story short, the quoted replacement cost could be just the tip of the iceburg.