Jill, I thought I'd try some detective work for you. I'm not sure I got anywhere, though.

The nearest entry on the IGI for Thomas is the one baptized 29 Jan 1814 son of Thomas KEWLEY and Isabella CORRIN at Douglas St George. This couple married 26 Apr 1808 Braddan, and they had a Jane in 1809, another Jane in 1814 (same day as Thomas), and a John in 1817. Does this match up with what you have?

You're right, there isn't a marriage turning up for Thomas Kewley and Elizabeth, which likely is just before the start of English Civil Registration. Their first child Elizabeth is in the FreeBMD for Dec 1837. If you order a certificate, you'll obtain the mother's surname.

I noticed that Thomas & Elizabeth Kewley had two children in the 1861 census (Helen age 17 and William age 15) that ought to have been in the 1851 but weren't with them. They ought to be somewhere, so maybe they're with relatives?

Working with Helen first, FreeBMD's has two Ellens and a Helen born 1843-44, and the IGI has an entry to match one Ellen and one Helen, neither of whom is the one we want. The IGI seems to have only one of Thomas & Elizabeth's children, the first one Elizabeth 3 Jan 1838 St Peter Liverpool.

In 1851 there is an Ellen Kewley, Niece age 7 Scholar born Liverpool in Tranmere. The Head is Charles Ashton 44 born Liverpool and his wife is Sarah age 40 born Douglas. This entry has a lot of people including their 3 daughters, a brother Richard Ashton, 4 visitors and 2 servants. According to IGI, Charles ASHTON married Sarah KEWLEY 12 Aug 1829 St Martin's Liverpool. That means Ellen is a niece on Sarah's side. The only Sarah Kewley b IOM on the IGI that's close was bp 16 May 1808 St Mathew Douglas d/o John KEWLEY and Ellinor COWIN, and she had a brother Thomas bp 9 Nov 1810 St Mathew. That's about 3 years too early to match your Thomas, so this isn't a good candidate. This may be the wrong Ellen Kewley.

I got nowhere looking for the other child, William. The two children could be together, and the Kewley name mis-transcribed on Ancestry. Findmypast hasn't transcribed Lancashire for 1851 yet, so can't check there.

I don't envy you on this one. It's a challenge!