I'm also wondering about the 1901 entry. Marie Winifred was born Dec q, 1899, West Derby (a part of Liverpool), so she should show in the 1901 census. So far, I've not found her in England or Wales - even a search on Chandler without a first name b.1900 +/- 2 years , doesn't bring anyone up that looks like her.
I'm now pretty sure that the Jessie W Chandler with Winifred on the 1901 is your Marie but the enumerator got the age wrong from the original schedule - instead of 1 he interpreted it as 7. I have checked the page and it is written as 7 but these mistakes did happen. The Jessie, I'm not sure of - maybe it was a pet name or, again, the handwriting was so poor that the Marie was mistaken for Jessie.
As an example of the Marie/Jessie confusion, I've just written Marie with a loopy M, as they used to do, and it could be interpreted as Jessie, maybe - see attached.
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