So far as I can see now you are dependent upon birth certificates - ideally Robert's but the problem is that there are quite a number of them around the approximate date.
There is, however, a George Bell registered Carlisle March qtr 1853 10b 361 which seems to fit both the George in 1861 with mother Margaret and brother Robert, also the George with same people and also Christopher Morrell in 1871 and also in 1881 with Christopher, Margaret and younger brother David Morrell.
You could put the proviso that the mother's name was formerly Bell/Porter and if it's wrong then they will refund part of your money. If you really wanted to you could also ask them to do a three year search, paying I think it's £11.50 to find you Robert's birth certificate with the parents names as you believe them to be.
As for the marriages, maybe Christopher and Margaret didn't marry? it wouldn't be unknown.
I wondered whether Margaret's name wasn't Porter, if her mother Sarah had been married before or even if she had been born illegitimately but there's no conclusive evidence of that in the 1841 census either, I don't think you have this
Kirkyate, St Mary, Cumberland - All born in County
Francis Porter 60 Sawyer
Sarah 45
Margaret 15
Sarah 3
David 2
HO107/176/7 12/18
Although with a gap between Mary and Sarah's ages like that it is possible and she became known as Porter later, maybe using her official name for her marriage.