Looks like Janette bc1845 later went by the name Jessie. (a few of her siblings named their children Jessie). She was still in Braddan in 1861, a servant.
Jessie married John Booth December Qtr 1870 Salford 8d 17. Jessie died Sep qtr 1872 Salford 8d 18.
Cant find her on 1871 Census but date of her death eliminates her from being Williams Mother.
Sandra