Hi there, Romwai
I think these are what you are looking for.

Rachell Rothwell age 2 years daughter of Joseph ansd Sarah Rothwell buried 7th Sept 1834 St Leonards Churchyard Middleton Lancashire
Elizabeth Rothwell age 8 years daughter of Joseph and Sarah Rothwell buried 8th Sept 1834 St Leonards churchyard Middleton
abode Middleton.
Buried by R C W Wilkinson Curate
Register 1829-1834 page 194 enrty 1548
Here is another additon to the Rothwell family.
Baptism
Elizabeth Rothwell Baptised 16th July 1826 Manchester Cathederal
Father Joseph Rothwell mother Sarah
Marriage
Joseph Rothwell married Sarah Poole
14th Aug 1820 Manchester Catherderal
additon to information
Baptism of Raechell Rothwell daughter of Joseph and Sarah Rothwell
Baptised 23 Sept 1832 baptised by R C W Wilkinson Curate St Leonards church middleton
Abode Middleton occupation Dyer
Cheers Ecclescake
Picture of this church can be found on the Lancs on line parish church aliong with plenty of church records.
Cheers
Ecclescake 2003
I found some more siblings
Joseph Rothwell Baptised 4th Jan 1824 St Thomas Church Ardwick Manchester Lancs
son of Joseph Rothwell occ Dyer and Sarah
Bapt by W Wordsworth Curate
Richard Rothwell Bapt 10Aug 1834 St Leonards Middleton Lancs
son of Joseoh Rothwell occ Dyer and Sarah
Bapt by R C W Wilkinson Curate