You may not think that the Owain Glyn Dwr rising had much to do with the House of York. However, Edward of York, the second Duke, was heavily involved in suppressing it, it had a major impact on his sister, Constance, and its effect on Wales was to play its part in influencing Welsh opinion during the Wars of the Roses. Given that Henry IV was responsible for the most brutal repression of the Welsh since Edward I was at his worst, including passing legislation that made the ethnic Welsh definitively second-class citizens in their own country, it seems a little odd that Wales became predominantly Lancastrian territory. But so, oddly enough, it was to be.
First, it's important to realise that Wales at this time was not a unified whole, more a geographical and cultural expression. It was divided into a large number of marcher territories, each of which was in effect a small kingdom with its own customs. These lordships did not have representation in Parliament, nor did they pay central taxes or receive visits from the King's justices. The King's writ did not run there. The royal territories in Wales were organised in a similar fashion, under local (usually English but sometimes Welsh) officers.
In the 1390s the marcher lords had become extremely efficient at squeezing money out of their tenants and at the same time tended to be absentee landlords who lived on their English manors.Though, as mentioned above, the Welsh did not have to pay parliamentary taxes, they were far more heavily burdened than their equivalents in England. Between 25% and 80% of the lord's income arose from the proceeds of justice - or what passed for it. The remainder came from various levies - for example communal fines, 'aids' raised when a lord entered his inheritance, and a sort of protection money paid by criminals immigrating from other lordships. Bolingbroke's relatively modest lordship of Brecon produced an income of £1500 a year on this basis. (For comparison the qualification for an earldom at this time was, theoretically, an income of about £667.)
The men of Wales often 'went as soldiers' and Richard II's peace policies created unemployment among this pool of men, and probably added to the discontent. In addition, at the turn of the century, many of the lordships underwent regular changes of ownership as their lords were forfeited, restored, or, as in the important case of the Earl of March, died a natural death. The effect was further disruption of a society that was already far from stable.
It was a case of tinder awaiting a spark, and that spark was soon to be struck.
Source - The most useful single source is The Revolt of Owain Glyn Dwr by R.R. Davies. A very highly recommended book.