My site is really only set up to deal with earlier enquiries (First World War, the 1911 census, and earlier) but in this case I may be able to point you in the right direction.
The London Gazette of 24th April 1934 reported that on 23rd December 1933 Walter Grover, Esq., died at his home of "Cattsdells", Hemel Hempstead, and probate was given to his son Lieutenant-Colonel Charles Walter Grover of the same address. Other records show he was aged 91. In 1937 a Mrs Grover (presumably the widow) was living at "Cattsdells", Redbourn Road, Hemel Hempstead. She may have been the Annie Grover who died aged 82 at Hemel Hempstead in 1939.
The Grover family were a well to do family of solicitors in the town and it is reasonable to assume that Cattdells was a very substantial house, with a large garden, which came on the market about 1940 and could well have been suitable for a small children's home.
If you look at a modern street map of Hemel Hempstead you will find a road called Cattsdell which is part of the New Town development of the 1950s onwards. It connects with a road now called Queensway - which before the New Town would have been called Redbourn Road.
I think that the Children's Home you refer to as "Cat's Tails" must have been "Cattsdells", a large house facing onto the Redbourn Road, Hemel Hempstead, which was demolished to make way for the New Town developments.