Is the lack of the definite article in the English translation (I had no option to put "the chapel" in - there simply was no box with "the") a matter of idiom?
I believe it is - that in Wales, one talks not only about going "to school", "to church", or "to hospital" but also "to chapel".
And that whether one goes "to church" or "to chapel" depends on one's denomination.
(Not just specific to Wales, I guess, but there's a fair number of them here): Or even within a single denomination itself; Plymouth Brethren churches are all the same denomination (although they tend to dispute that denominations exist), however, depending on whether they allow non-members to break bread changes whether they're a chapel or a church.
But also, what you wrote is correct too :)
i'r xxx is used for places that you go to regularly, on the basis that you usually go to one particular one. So, i'r capel, eglwys, ysgol, gwaith, ysbyty, (g)wely, ... in Welsh is usually 'to chapel, church, school, work, hospital, bed, ...' in English (without 'the').