It was their suggestion to help us, they chose the house.
So in essence, they bought an investment property, and you bought a share on a part-ownership basis. It's water under the bridge, and it doesn't help your situation to pick over the bones of what went before, but either you were all spectacularly naive or alternatively they were a great deal more aware of the implications than you. Given people who are spectacularly naive tend not to have seventy grand lying around loose when they're 45 (you mother's now fifty, the purchase was five years ago), I would favour the latter.
You're going to lose money by selling up, but I think your choices are limited and in any event are going to leave your relation with your parents a smoking ruin. You can either:
(a) do nothing, shout "fuck you, see you in court" and leave it to m'learned friends (expensive, ugly and very stressful)
(b) get them out of the stupid idea that they can remain on the deeds and buy them out at an agreed (how?) price (sensible, but it sounds like they don't want to be sensible)
(c) sell up, divvy up the proceeds (you all lose money) and then attempt to buy another house (will you have a deposit?)
In any case, your lessons are (a) get legal advice before doing complex financial transactions, no matter how much you think the parties involved are trustworthy and (b) tell your parents to fuck off out of your lives.