Hunt kennels is where they keep the hunting hounds. They often offer a stock dispatch and disposal service to the local area - and generally, will do a humane and sensitive job.
Re: dogs not eating pork - the kennels will feed meat raw. There used to be - and may still is, I'm not up-to-date on these things - a very rare but very lethal bug that was found in uncooked pork. Salmonella cholerei suis, or something of the such which. Because of this, people my age don't feed raw pork : although the risk of the meat carrying this bug is tiny, the consequences would be too great to take the risk.
There could be another reason, but that'd be my guess.