If you paid with your own money and it does happen to all go wrong (which it won't) then it's a lesson learnt - your parents can't expect you to cancel just because they are worried about it, if it's your money. You have the right to do what the hell you want in this case and you shouldn't feel pressured by them in any way, as that is just plain wrong.
If they paid on the other hand, then if they are threatening to cancel/get a refund, etc, then you do need to shown them some proof. In this case it's a shame they are getting like this so close to the end of it all.
I'd be concerned that if your parents are saying 'those circuit boards could come from a DS' then there is little hope of your convincing them that anything is moving along. It sounds to me like they don't want to hear any different, that at the back of their minds, they can see that it is a real project and not a scam yet still want you to cancel for whatever parental reasons they have (waste of money, etc). The Pandora boards are obviously real, just look at all the different photos, and they are obviously not from a DS or other device. I don't see how it's possible to think otherwise except if pretending to be 'blind' to the whole thing.
Don't fall into the trap of being pressured by your parents into cancelling if you feel the evidence is strong enough to show that it is a perfectly legitimate project that will deliver. If you can see this given the information available to you (images, updates, etc) then there is no logical reason why your parents cannot also see this. I'm betting that they have another reason for wanting you to cancel and are using as many excuses to do with the project failing/being a scam, as they can find to justify you cancelling your order.
[edit] Also, if the unofficial blog isn't good enough, I doubt a list from here will be any better. Have you tried showing them videos off youtube, from the first steps of working boards, to prototypes assembled in rough cases, testing of nubs, etc?. That's evidence enough to show development. The official developer blog should also be enough: http://www.open-pandora.org