You've got the name of the regiment slightly wrong, and at the the time in question it had two battalions, your dad was in the 2nd Battalion, which returned to England in 1948 and later in 1948 it was amalgamated in Austria with the 1st Battalion and both battalions became the 1st Battalion.
From 1945 to 1948 the 1st Battalion was in Austria and from 1948 to 1953 it was in Germany then it went to Malaya until 1953
Your dad's unit was 2nd Battalion The West Yorkshire Regiment (The Prince of Wales's Own)
( formerly the 15th Regiment of Foot )
In 1958 the regiment was amalgamated with The East Yorkshire Regiment (The Duke of York's Own) and became The Prince of Wales's Own Regiment of Yorkshire
In 2006 The Prince of Wales's Own Regiment of Yorkshire was amalgamated with two other regiments to form The Yorkshire Regiment
Your dad's former regiment is now 2nd Battalion The Yorkshire Regiment aka ( 2Yorks )
The Regimental Museum of the Yorkshire Regiment which includes it's predecessor regiments is now housed in the York Army Museum.
http://www.yorkshireregiment.com/museum/The museum has a research service.
There is also a Regimental Association
http://www.army.mod.uk/infantry/regiments/25668.aspxhttp://www.yorkshireregiment.com/If you haven't already got a copy of your dad's service record, you can get one from here...
https://www.gov.uk/requests-for-personal-data-and-service-re...