It sounds like you need to go back to the very basics - what do you definitely know about her?
Where did you first come across her? Do you know her parents? Her place of birth?
These children of hers - how did you find them, obviously not from the 1841 census if you are now doubting that is the right family.
Go one step at a time confirming things as you go. Dont use something as a step to the next thing unless you are sure of it (like a family on a census) because if ti is the wrong one, you will go further down the wrong trail and it will be harder to sort out the right from the wrong.
By the way, ages for adults on the 1841 census were rounded to 5 years. But unlikely John would be rounded from 20 down to 15!
What workhouse was she possibly in, in 1841?
If William was born Dunmow in 1839, was it far away?
I found what looks like William's birth in the indexes, JAS quarter 1839 ref X11 41, Chelmsford area.
If his mum did die in 1843 in Dunmow, I wonder what happened to 4 yr old William?
Think you may have to get some certs to prove each stage of this one, cos it is a common name.