Realistically, how much bandwidth will your parents use on the other computer? Are they going to play online games as well? Download very large files? If not, then you will notice no real difference in your connection speeds and pings, IMO. A router will share the bandwidth, no just halve it. So when they are not using their connection you will still have full bandwidth.
You could try it and see. All you would need is a cheap router and a couple of NICS and some cat5 cables. Pretty cheap compared to a second phone line or even worse, second DSL connection!
So I suggest you try it. If they do so much stuff on the net that it annoys you, you can always turn them off, I suppose.
Or only allow them on the net when you aren't. That sort of behaviour.
Or, you could share your toys like you should. IMO, anyway.
Cheers
Mick