Hello ednalou,
FreeBMD has a birth for Frederick ATYEO in the March quarter of 1865 in Bridgewater Registration District. Volume 5c, page 197.
There is another entry for a birth of Frederick ATYEO in the same RD in the December quarter of 1867, volume 5c Page 389.
It might be worthwhile obtaining the certificate of the 1865 one if you are sure of that year.
FreeBMD also has the births of Polly ATYEO in Bridgewater RD in the June quarter of 1864.
There are entries for Ellen ATYEO in Bridgewater in June quater of 1865, Volume 5c Page 482 and September 1865, Volume 5c Page 436.
I cannot see anything for a Mary ATYEO.
Jo.