Dear LA (do you have a forename - it helps me to be politer!)
When you say you don't know much about the AINSLEY clan except that they live in Stockton/Billingham, is this what you've been told about your specific ancestor Thomas, or is it general information you've gathered elsewhere?
Firstly, Stockton, being a growing industrial town, attracted folk from all over a bit like filings to a magnet, and in 1881 there are at least 4 unrelated AINSLEY groups there along with several related families, and the situation doesnt improve much from there on.
To really help you, I need to know more: what research have you done so far - indeed - where in the world are you researching from - it governs what information is readily available!
Have you yet searched the GRO indexes for Thomas and Hilda's marriage, gor their marriage certificate, and thence discovered who his their fathers were - this has got to be the first thing!
Once you have Thomas's father's name, there's a very good chance I can locate him, since I ahve a lot of data on the Stockton AINSLEYs - but the problem is that what you've said so far doesnt give much clue!
Please contact me directly with any other info you have - we can post results here for interested persons - and at least I can point you at where to research to gather more data.
I think its unlikely that you're scions of the best researched AINSLEY clan (the Bilsdale AINSLEYs) since the data doesnt fit known persons, but having tied in a family in Australia only this morning, its quite possible its one of the "escaped" lines!