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I don't have any details of Jemima of the Burslem family but this might help.
Jemima Mountford (baptised 1789 at Norton), married 1820 to Joseph Jones at Norton. Daughter of Joseph and Ann Brindley.
Jemima baptised 1829 at Norton - daughter of (Joseph the son of Joseph above)and Mary Sherratt. 1841 and 1851 with parents and siblings (no Sarah) at Lower Stone House Farm, Brown Edge. Not followed up on Jemima after1851 but parents and other siblings were farming at Endon in 1861 and 1871. Eldest son Hugh took over the farm on the death of his father and by 1891 Hugh, with his own family, were farming at Barlaston.

Both streets are in Hanley, Stoke-on-Trent and I suspect that Austin Street is in Eastwood whilst Botteslow is  possibly in St Lukes. The streets are within a 10 minute max walk of each other.

www.oldmapsonline.org is the site which is free and there is no breach of copywrite.
When the page opens, a map of a wider area of Stoke-on-Trent appears which you can manipulate to move to the area which includes Fenton & Eaton Park. Then, on the right hand side of the screen, a number of Ordnance Survey maps appear made over different years. I chose the 1898 one which is the nearest to your 1901 Census date, but you can look at all of them without logging out. Best of luck.

If you haven't visited yet the following might help. The south end of Botteslow Street meets Leek Road where if you turn right for 50 yards you will see Trentmill Road on the opposite side. The name gives a clue to it's past, as at the bottom of the road was on old flint mill (now demolished) powered by the River Trent. The river here is more of a stream than a river. At the bottom of Trentmill Road there is an unmade track which goes over the river bridge, then under the railway bridge, before climbing a hill. The land on the left was part of the farm, and at the top of the track there is a T junction and the farmhouse entrance was located to the left. I believe that the farm originally formed part of the Berryhill Colliery estate prior to nationalisation in 1947. The colliery closed in 1962 and the site is now an industrial estate. I guess that the farmhouse was demolished in the 1970's when it was occupied by 2 unmarried brothers whose surname was Shufflebottom.