Ref, you're right. The 'd' is pronounced with the tip of your tongue touching the teeth very lightly and briefly so that some air can escape at the edges. It's close to a soft 'th'. (I doubt that's a better description than yours!)

Also, the 'rh' is an 'r' preceded by an 'h' - one could say the two letters are reversed in pronouncing them. I'm not a Welsh-speaker but colleagues at the Welsh school where I once taught tried hard to drill some Welsh into me. Some of the pronunciation was the only thing that stuck.

And yes - 'Farewell to the Rhondda' is an entirely different song.