I can endorse Microscopisr's recommendation of a trip to Mount Stuart. It is accessible as a day trip from Glasgow - train to Wemyss Bay, ferry to Rothesay and bus to Mount Stuart, with either a pleasant strll or a minibus ride to the house. It makes for an excellent day out. I would suggest, however, that its twin is not so much Dumfries House (possibly a great-aunt) as the Marquess of Bute's other property, Castell Coch, near Cardiff.
I'd consciously put "twin" in inverted commas for shorthand avoiding a slightly more complex sentence. The three; Cardiff Castle. Mount Stewart and Dumfries House are closely linked. Cardiff Castle seems to me to be the more senior of the three and seems to have contributed wealth and facilities to both Mount Stuart and Dumfries House; largely derived from the Port of Cardiff and its hinterland. The development of Dumfries House and estate by the now King Charles has been a quite remarkable boon to the locality providing both employment and training facilities to a relatively underprivileged area. In the early days my son was Head Chef at the Cook School in Kilmarnock and alongside the Prince's Trust took on two cohorts of youngsters from some to the more deprived areas of Kilmarnock and trained them - he found jobs for all but one of them. At the end of training one of the cohorts, he used these youngsters to prepare a meal for the then Prince Charles and some very wealthy people from around the world. Dumfries House now have their own hospitality training facilities along with other training opportunities for local folk.
Talking of Kilmarnock that is another hymn tune with carpet connections, for around 80 years BMK (Blackwood & Morton, Kilmarnock) were major carpet producers and employers in Kilmarnock.