Combination RS Best of Ireland and Scotland in June 2027

The most important factor is unknowable until the 2027 tours and dates are released in mid April. I haven't done any back to back tours, but people who have recommend a day or 2 between to decompress.
The order doesn't matter as much as finding 2 that fit together time wise.

There was a recent thread on taking the Heart of (not the Best of) tours back to back.
https://community.ricksteves.com/travel-forum/ireland/back-to-back-ireland-scotland-14eb48f7-b65c-4f96-8ae1-c9540047cf8d
The previous commenter is correct that it will depend on the 2027 tour dates. This year, the Ireland tour doesn't have a start date in June until the 26th, while the Scotland tour has several start dates in June. Still, you could buy a RT ticket BOS-DUB and add the connecting flights, which are likely to be quite inexpensive. For something a little different, you could take the Belfast-Cairnryan ferry and connect by bus/train to Glasgow.

I have a General thought having done several back to backs or back to back to backs (yes, I did 3 in a row one time!). I found that I enjoyed back to backs more when I changed cultures or big city to smaller towns for my tours. I loved doing Best of England + Paris and the Heart of France. I didn't enjoy doing Southern England + Scotland as much because there was more commonality. I never thought I'd get tired of seeing castle ruins but yes, I did on that set which surprised me very much.

My 3 in a row was the 21 day Best of Europe which ends in Paris, then the Best of Paris plus another week there then Village Italy. Even though I'd spent time in Italy on the 21 Day tour, the Village Italy locations gave it a different feel from Venice, Florence, Rome.

Each person is different and the similarities between Ireland and Scotland might appeal to you. I don't think it matters which you do first. I have done both of them but that was before Covid and the itineraries for both have changed a little bit.

IF the dates work for you, try to give yourselves a day or 2 break in between the tours just to get laundry done and to get your tour mates out of your head, hahaha.

Yes, I would arrive a few days before the 1st tour- probably Ireland and stay extra at the end and a few more at the beginning of the 2nd tour probably Scotland and again at the end. Thereby adding 8 days to Ireland 7 days and Scotland 8 days.

My concern is how similar are the two tours. When I read the itinerary they sound complimentary.

Pam makes an excellent point about changing cultures or tour types.

After the Best of Ireland tour you could easily fly from Belfast to Paris for the Heart of France tour or Barcelona for the Best of Spain tour, for example.

Or combine the Best of Scotland with a different tour.

Nonstop flights within Europe are fairly inexpensive.

We did back to back, Best of London 7 days and Best of Scotland 13 days.
1 day easy travel time by train London to Glasgow.
It can be done. Only 1 hotel all of London tour switching to moving 1-2 nights hotel around Scotland. We were tired by end of 22 days but so worth our time there.