adre is actually an adverb - 'homewards'. 'Homewards' is uncommon in modern English so it is just translated as 'home', with the interpretation that it involves movement towards home. So as EllisV says, it does not need a linking yn in front of it.
It is a contraction of the older expression tua thre which is still used in some dialects. In the Gwentian dialect (y Wenhwyseg) of south and south-east Wales it is often pronounced /sha thre/, especially by older people or those keen to continue the dialect.
(tua thre meant 'towards home' - tre has nowadays come to mean 'town', but in the older language it was perhaps more like 'homestead'. 'Towards' is often tuag at nowadays if movement is involved)
Wow thanks, that's really interesting! Did old welsh ever use a derived version of the proto indo-european word "dom" to mean house or home?
According to the GPC, tref may have come from IE *(s)teg, possibly meaning 'dwelling place'.
Not a field in which I claim any expertise, though!
No, since "yn" in it's verbal particle form is only used to connect a form of "bod" to a verb-noun, noun or adjective, not a place and even then this sentence would have the "yn" between the "ti" and the "eisiau" if it did have an "yn" except "eisiau" doesn't take "yn".
Is adref really a typo? I have seen this version of 'homeward' written in several places even though (i believe) the f is mute.
No, adref is fine here - it is already in the database as an alternative answer.
Off topic, but can any Welsh speaker please explain to me the difference between 'Cymraeg' and 'Cymreig'? Diolch yn fawr iawn.
This is explained in the notes for the earlier section 'Work 1'.
This explains how to find the notes - https://forum.duolingo.com/comment/17638579 The notes for 'Work 1' are here - https://www.duolingo.com/skill/cy/Work-1/tips-and-notes