I'm not quite sure what you mean, but am guessing you mean is there any way to prove the Peter who is mentioned as dying in 1850 is your Peter? Is such a pity the OPR didn't state "weaver", then we'd have him sorted... but that's life, and OPRs! He was clearly alive in 1847 at the time of his wife's death, but if there is no sign of him in the 1851, then it would appear the chances are high that your man died in that 4yr period.
I really don't think there would be many, if indeed any, other Peter Elders around the same age in Cupar given it is a small town. The fact that you mentioned the childen were staying with their aunt in 1861 would suggest too that both their parents were perhaps dead by that time.
There are no Elders in the published MIs for Cupar, which is odd, given that there were several families of them around, but thats just the way it goes sometimes.... lair records might be worth following up. Lair registers dating from 1868 are administered by Fife Council, Cemeteries Department, County Buildings, St Catherine Street, Cupar, KY15 4TA. Tel. 01334 412818. Fax 01334 412896. Although this is later than the period you are interested in, they would probably be able to advise you about the earlier records.
There does not appear to be a will on SP - that would be my next port of call, but that does not mean in itself that no will was written. I've certainly found several testaments now which are not indexed, but certainly exisit!!
However, there is one for David Elder, who you thougth might be a brother:
Elder David 04/11/1897 Mason, Newtown, Cupar, d. 13/09/1897 at Cupar, testate Cupar Sheriff Court SC20/50/75 (3 pages)
I looked up "Fife Shop Keepers and Traders 1820-1870" yesterday. Its one of David Dobson's hugely helpful series. However, no sign of your Peter, just Elders the Bakers.
There will be something somewhere, I'll keep thinking, but it could take a lot of time and good luck to track down...when were you planning to visit Scotland??

http://www.fifefhs.org/
Cupar Library are also very helpful and will usually help those from afar with specific research queries. They also have microfilms of the local papers which may yield something, maybe. Some of the obits are in book form, so I'll have a look at those next time I'm in.
http://www.genuki.org.uk/big/sct/FIF/li ... ar_lib.htm
Also worth maybe contacting NAS., as they have a LOT of archive material.
http://www.nas.gov.uk/
Also, if you PM me with your email address, I'll send on the photos of the houses. Oh duh,

Best wishes
Lesley