Compared to most parties in Northern Ireland the DUP see the province as in integral part of the United Kingdom and get involved in Great Britain/England only issues more than the other parties in Northern Ireland do.
If a formal coalition does happen I would think that there will be times that the DUP will take an interest in National Rail.
Not saying much considering only two political parties won seats in NI, and one of them doesn't take their seats.
The DUP consider themselves and NI as an integral part of the union but also as a Different Place and not at all like Britain; they take pains to refer to NI - constitutionally correctly - as a "province". That's why they can be very intolerant of gays, women, Muslims (but they'd "trust them to go to the shaps"), why they can say eff you to binding political agreements and why they're suckling on the teat of the Orange Order, and Ulster's three primary *banned* loyalist paramilitary groups. The DUP exhibit a herronvolk mentality and are exclusively concerned with their six county province and how much money they can funnel into it (no doubt to the primary benefit of Unionists in the east).
This is a fantastic situation because for once people in England are remembering that NI exists, Googling who the DUP are and rubbing their eyes in disbelief.
The only UK-wide issue the DUP really care about and campaigned on is Brexit, alongside some fundamentalist Presbyterian issues like opposing gay people getting married, etc. The DUP actually got quite priapic about hard Brexit during the campaign and that's what they wanted until the referendum passed and they realised that would be a Dumb Idea.
I think the idea of the DUP having any sort of opinion at all on National Rail beyond maybe SailRail to Belfast is a bit fanciful and naive.