I think I can add a bit more to this. I'm a keen researcher of my own surname and I believe that the Margaret Wilding mentioned in this thread is a first cousin, four times removed.
Garstonite is right about another marriage complicating things. Richard Whittle married Ellen Wilding on 6 Feb 1837 at Preston St John. Being early in 1837 this marriage doesn't appear on LancsBMD. Ellen is not a relation of mine AFAIAA, but using LancsBMD and census returns I believe the marriage produced at least the following children :-
Jane b 1840
William b 1843
William b 1845
Richard b 1847
William b 1850
Ellen b 1852
The first two Williams died early, but the others survived infancy.
I think that Robert and Margaret had a total of 11 children, so the original poster's concern about the parents might be alleviated somewhat. The ones who survived childhood and who are therefore not mentioned on the MI are
David b 1852
John b 1854
Mary Elizabeth b 1856
Richard b 1861
Ann b 1869
But there are still some loose ends that I can't explain :-
1) The baptism record on IGI (which is extracted, not submitted) states that Mary Elizabeth Whittle died in 1858. Census returns suggest that this wasn't the case, and there are no matching death records on LancsBMD or FreeBMD.
2) There are two William Whittles with a mother's maiden name of Wilding in 1850. I can only explain one of them. Registered twice ?
3) IGI shows a Joseph Whittle baptised in 1861, son of Robert Whittle and Margaret. Was this a re-baptism of the 1859 child, who survived until the age of 15?
AND FINALLY, I'd love to see the full detail of the MI mentioned by the original poster. If he/she or anyone else has this could they please let me know.
Tim Wilding