Re- the port where the ships sail for Ireland- the modern port is at Cairnryan- but both those terminals (a mile apart) are modern- P and O for Larne, and Stena for Belfast.
Historically the ships sailed from Stranraer- the railway station is where the port was, but there is little or nothing to see there now.
However, before Stranraer port was established, there were two other ports for Ireland- Portpatrick and Isle of Whithorn (about 4 miles south of Whithorn), so it depends what you are looking for and what time era you are looking for.
My guess is that if the family lived in the Wigtown area they would have sailed either from the Isle of Whithorn, or possibly even the port of Garlieston (better known for it's connections to the Mulberry Harbours in WW2).
Have you done any genealogical research on Scotland's people, or contacted Dumfries Archives (in the Ewart Library)?.
All extant BMD records for your family will be on Scotland's People.
The reason I am asking is that, on searching CALM, I don't see anything at Dumfries regarding Kirk Session records, or burial records.
If the original Kirk records are not held locally, I wonder if they are in fact in Edinburgh- not that you need to view the original registers.
You should be able to search Scotand's People for free at the Ewart but their website doesn't explicitly state that.
There are quite a number of graveyards between Wigtown and Whithorn- several of which are at the former sites of the Churches they serve.
Do you know that they were never in the larger town of Newton Stewart, a few miles east of Kirkcowan, and where you would normally turn off the A75 for Whithorn/Wigtown?
In Dumfries itself I recommend the Dumfries Villa Guesthouse- Colin will look after you very well there, and he has a deal with a local restaurant to get 20% off what are already good prices- and will make bookings there for you.
From Dumfries it's a straight drive down the A75- a very good highway- to Kirkcowan. You should do it in under 90 minutes although you will have passed a number of places you really should visit on the way.
From Kirkcowan to Wigtown it's only another 15 minutes or so, another 5 minutes to the distillery, and Whithorn is another 15 minutes or so further on. Kirkcowan to Stranraer is about 30 minutes.
At Whithorn I would suggest the Steam Packet Inn at the Isle of Whithorn as somewhere to stay, and also, for lunch, suggest the Community Cafe at the Isle.
At Wigtown, apart from bookstores and the Kirkyard, you really should visit the Martyr's Stake/Memorial- a vivid reminder of the time of the Covenanters in the area.