Hi Sue
I'm not sure how much family information you already have and although I have nothing definite, this stuff may help you along a bit.
If your grandfather was a policeman by the 1920s and assuming he wasn't actually called Alfred, one of these people is quite likely to be him. The information is freely available to search on the 1911 Census website -
www.1911census.co.uk - but I'm afraid everybody has to pay to look at the detail.
KINDER FRED M 1876 35 Dartford Kent
KINDER FRED M 1903 8 Barton upon Irwell Lancashire
KINDER FRED M 1895 16 Ashton under Lyne Lancashire
KINDER FRED M 1884 27 Burnley Lancashire
KINDER FRED M 1900 11 Saddleworth Yorkshire West Riding
KINDER FRED M 1876 35 Huddersfield Yorkshire West Riding
KINDER FRED M 1891 20 Huddersfield Yorkshire West Riding
KINDER FRED M 1876 35 Huddersfield Yorkshire West Riding
KINDER FRED M 1867 44 Huddersfield Yorkshire West Riding
KINDER FRED M 1897 14 Halifax Yorkshire West Riding
KINDER FRED M 1908 3 Bradford Yorkshire West Riding
KINDER FRED M 1889 22 Bradford Yorkshire West Riding
KINDER FRED M 1869 42 Leeds Yorkshire West Riding
KINDER FRED M 1910 8/12 Hunslet Yorkshire West Riding
KINDER FRED M 1871 40 Pontefract Yorkshire West Riding
KINDER FRED M 1866 45 Ecclesall Bierlow Yorkshire West Riding
There are also plenty of marriages listed on the FreeBMD site for both 'Fred' and 'Alfred' Kinder that you could check out -
www.freebmd.org.ukLydgate is next door to Mossley, and there are two death records registered on the Cheshire BMD site -
www.cheshirebmd.org.uk. One is for Stanley Johnson in 1971, and the other for Annie Johnson in 1969.
JOHNSON Annie (age 65) registered at Ashton and Mossley, Tameside Reference: A&M/8E/68
JOHNSON Arthur Stanley (age 80) registered at Ashton and Mossley, Tameside Ref: A&M/14E/113
Of course it's entirely possible that neither of these deaths are the people you're seeking, but it might be worthwhile checking properly because, if Annie's death was indeed due to suicide there would automatically have been an inquest and, therefore, a Coroner's Inquest plus a Coroner's Report.
The bad news is that Coroners' Reports in England & Wales are usually 'frozen' for 75 years, so you might have to wait a while, but the good news is that the death certificate might at least provide you with a precise date, cause of death, and an address. That might equally rule her out of your search, so time saved.
Since newspapers tend to go for the more sensational stories, there could well have been a report about the circumstances of her death in the local paper, especially if the dog also fell victim. If you can, and have the time to search back editions of the Oldham Chronicle or similar, that avenue might well be your best bet so the date of death could again save you hours of potentially wasted energy.
From the above death certificate, Annie's date of birth would have been approximately 1904. The Lancashire BMD website -
www.lancashirebmd.org.uk - lists plenty of births within the right timescale for both Annie Whitehead and Annie Bradbury, but none for Annie Kinder. Since the on-line Oldham birth records on that site also provide the birth mother's maiden name about 70% of the time, you might be able to pick up further clues.
Woody