As you may know there is only 1 Emma Bateman listed in the 1871 IOM census:

Emma Bateman aged 4 (born c1867) Born Wales Living in property no. 60 in the parish of Lezayre (Sulby Glen/Glen Moar?)
Mother: Sarah Bateman aged 37 Born Wales, a 'House Keeper'
Siblings: Marria 10, Ann 6 both born Isle of Man
No father shown.

Strange that the youngest daughter was born in Wales...

Interestingly Sarah has a number of boarders who are all 'Slaters' a couple of whom are Welsh, the rest Irish. Property No. 59 also has some Irish Slaters boarding with them. Perhaps Sarah's husband was connected to the Slate Quarrying industry?