I found your reference to a Teather family in Bolsterstone from a search engine. I've been working on a Teather world-wide family tree for several years now, and have a web site (Link broken) dedicated to it.
I don't have a direct link to this Teather family, but I may have some helpful information. First, the "Teather" and "Tether" surnames where somewhat interchangeable around the 1800's, and they cross paths often.
The largest branch of the "Tether/Teather" family seems to originate from Nottingham, although there are some links to the Sheffield area.
The Ollerton reference is interesting - I have Edward Tether (b.1694 Bilsthorpe, died 1765 Ollerton) who married Mary Pinder in 1720. They had eight children at Ollerton between 1721 and 1738. Excluding females and infant deaths, they had:
1. Luke Tether (1721-1767), who married Elizabeth Peatfield - they had 5 children at Ollerton, the eldest two being sons Benjamin (b 20/3/1750) and Thomas (b 11/11/1759). I have no info on descendents.
2. William Tether (b.1729) who married Ann Hall in 1755 at Boughton.
3. Thomas Tether (b. 9/5/1731) at Ollerton.
4. John Tether (b. 1734 Ollerton), who married Sarah in 1769 and had 5 children (but only one surviving son, William, who married Ann Salmon and Sarah Hurst and had 5 children between them. Of their sons, only Richard (b 4/5/1800) was born at Ollerton. Richard married Mary and they had a son Richard, born at Cuckney 17/10/1822 (there may be more).
Richard (Jr.) had two sons, William Thompson Teather, and Walter Teather. Here's the interesting bits: both these sons are listed as "Teather", and Walter lived as Eccesall (Sheffield) , not too far from Bolsterstone.
So while I don't have a direct link, I suspect your Teather family is related somehow. If there's anything else I can provide, please let me know. And please keep in touch!
All the best,
Kinburn, Ontario, Canada