Hi Marna -
The Otley Show, the oldest and biggest single day agricultural show in England, takes place on May 19th 2018. Otley is reachable from York by train to Leeds, Wharfedale line train to Menston and then connecting bus into Otley (bus is usually there to meet certain of the trains). There is show jumping (equestrian), livestock exhibition and contests (unsure about sheepdog trials as they are usually separate contests) and various stands and exhibitions. I enjoy the 'sheep show' (who knew sheep could be so entertaining?!), the birds of prey if they are there and because I'm a Yorkshireman, the ferrets! It's big, starts early and once the main show is over there a funfair for the youngsters - the farmers and older persons retire to the pub, which Otley has plenty of! See www.otleyshow.org.uk.
As for jousting, the Royal Armouries in the centre of Leeds has its own tilt yard for jousting and mediaeval fighting contests (knights in armour) but the events calendar on The Royal Armouries website only runs up to April of this year so far. Might be worth further investigation. Again, Leeds is rapidly reached by frequent trains from York.
For further events you could try 'agricultural shows North Yorkshire 2018' - I got a list of shows for the year, but am unsure of whether any further shows take place while you are in the north of England.
Hope some of this might be useful. I might add the Otley is only three miles down the valley from my own home!
Ian