Hi Moss, I've found an Ada with parents John and Lucy(the only other was in Mansfield)but not the brothers you mention... ROSS...RG13/2475 John Smith Head 36 Clodock Lucy Smith Wife 37 Kington Lucy 7 Alfred 5 Ada 4 Mary 2 Thomas 11 months Hope this helps..
In trying to find Ada Smith I thought I had narrowed it down to two suspects, with the one I posted being the most likely. Now I'm not so sure as I didn't know about the other children you named.
According to freebmd the only other Ada (middle name catherine) was born in 1895 in Ross, (maybe she was the one in Mansfield?) Unfortunately no one in the family remembers the names of Ada's parents so I'm working in the dark a bit.
Thanks for the pm. When I'm more certain who I'm after I'll get back to you