Upcoming Scotland trip itinerary advice

I recommend a day trip from Edinburgh to see the Falkirk Wheel and the Kelpies. I don't know who does these. Maybe Rabbies?
As far as I can tell, Galashiels is only an hour by train from Edinburgh but has no direct connections to any of the other places you're talking about visiting. I appreciate that two of your party have a booking that likely can't be changed, but I don't know if I would troop the whole family down there for two nights for this purpose.
For the remaining time, I would choose whichever ancestral place you have the most information about (e.g., where the headstones are, where the family home is/was) or otherwise looks the most interesting. If you can do it as a day trip from Edinburgh, all the better. For a stay as short as yours, I wouldn't change my accommodation at all.

Hi, for the May 28th day, you might consider taking a Rabbies tour (since you won't have a car) down to the border region, as tthere is one that goes to Melrose Abbey: https://www.rabbies.com/en/scotland-tours/from-edinburgh/day-tours/rosslyn-chapel-the-scottish-borders-short-day-tour

There are also some that take you to Alnwick Castle in Northumberland and the border region, and another that visits Stirling Castle (although that is easily done on your own from Edinburgh by train). These are all the one-day tours that Rabbies offers from Edinburgh: https://www.rabbies.com/en/scotland-tours/from-edinburgh/day-tours/rosslyn-chapel-the-scottish-borders-short-day-tour

With regards to May 29th, Dundee is nice and easy to get to by train (and you have the wonderful V&A museum location there), but of course, the Pitlochry/Perthshire area is also a treat, and you can get there by train. That said, I don't know how easy it would be to get around that area; although I'm sure there are buses. Stuart (isn31c) should know more about public transportation in that area and will probably pop in at some to give you some good advice.

Renfrew has lots of buses from Central Glasgow although the fun way to get there is the Renfrew ferry across the Clyde. It is meant to run to a timetable but last time I did it I had just missed a trip but he came back over to run a special trip for me. I must have been looking haggard that morning as without asking I was charged the pensioner fare. Anyway in Renfrew Town Hall there is a free museum open 10 to 4 Monday to Friday- Renfrew is a Royal Burgh.
Lanark also has a free museum (or it used to be) open 12 to 4.30 Friday and Saturday, but at other times by appointment for research. You get there by commuter train from Glasgow Central Low Level.
And there is also New Lanark Mill Village which is a UNESCO World Heritage Site.
It's kind of difficult to advise on Perthshire without knowing where in the County. But Perth city is much neglected on this forum. You should visit Perth Museum. Among other things there is the Stone of Scone, or the Stone of Destiny- used at every Coronation (including King Charles) since the year 1249.

Galashiels is only an hour by train from Edinburgh but has no direct connections to any of the other places you're talking about visiting.

That isn't strictly true.

For Abbotsford catch the X95 bus from Galashiels to Archies walk. The bus goes every 30 minutes and the journey takes 6 minutes. It is then about a ten minute walk to Abbotsford house.

There is a choice of several different buses between Galashiels and Melrose (51, 60,67,68) which drop you off at the abbey ruins. The journey takes about 20 minutes. Check timetables here. When in Melrose, there are two rather nice small gardens near the abbey which are worth visiting - Harmony Gardens and Priorwood Gardens.

You can also use the 68 bus to get to Jedburgh which is an attractive Borders Town and you could easily spend a day there. There is a Blue Plaque trail to follow round the town. Do make sure you visit the ruined abbey and also Mary Queen of Scots House. Greyfriars Garden, through a gateway on the far side of the Co-op car park is a lovely place to drop out on a nice day. On the edge of the town and about 10-15 minute walk from the Abbey is Jedburgh Castle and Jail Museum. If you are still feeling energetic, there are other short walks you can do from Jedburgh, although some can be muddy after rain. . Have a look at the brochure here.

If you want a castle, Then the easiest is possibly Thirlstane Castle near Lauder. Catch the 51 bus from Galashiels and get off at Factors Park and it is a 10min walk.

Thank you all for your advice!

@G3rryCee - I appreciate you bringing up the Falkirk Wheel and Kelpies. These sites have been on my radar and would love to see the Kelpies. My question is if a formal tour is absolutely necessary? I thought depending on where we are coming from it might be possible to add a stop there on our way back to Edinburgh on 5/29.

@Mardee - Thank you for your response regarding Rabbies Tours. I looked into some in my initial planning but will do a second pass to see if any of these align with our dates.

@Wasleys - It is a big help to get the specific bus numbers/routes, thank you! We will likely buy a 4-day Spirit of Scotland or Central Scotland Rover ScotRail pass. Does that sound right to everyone?

@isn31c - This is all very welcome information! As you say, some of these areas are not as frequently discussed on the forum. I appreciate the suggestions and am glad to hear there will be sites of interest to visit wherever we go. It has been difficult to decide as Scotland has so much to offer! We currently live in Colorado and Wyoming in the US and get quite a bit of time in the mountains. I would love to visit the Highlands and Cairngorms National Park but perhaps for this trip it would be beneficial to focus on Dundee with the seashore and V&A museum or delving further into the villages of our ancestry.

As someone who spends 2-3 months in Dundee every year, let me say that I propose you spend the extra time in the Highlands.

Dundee has the V & A, it has the Discovery museum next door. St, Andrews is only 13 miles away and easily accessible by public bus that run frequently.

However, my vote would be for the Highlands. The scenery is absolutley beautiful.

I'm always ambivalent on whether Spirit of Scotland is worth it's money, but I suppose it depends on how flexibly you want to travel.
If you don't go north of Dunblane (between Stirling and Perth) a Central Scotland rover may work better (and the Stagecoach X routes take you on from there to Perth, Dundee and St Andrews, also the 15 on its scenic Stirling to Perth via Crieff route and McGills X10 to Glasgow via the Trossachs.
Dunblane is interesting in that it has one of Scotland's Cathedrals which is never mentioned here. As a Presbyterian Church the Church of Scotland doesn have Cathedrals, but inherited pre reformation ones which have never been renamed.
Glasgow and Edinburgh St Giles are others. Anyway Dunblane is worth a visit. As a Brit the sombre side of the town, which I can't forget, was the Dunblane massacre of 1996. Read up on it, and say a prayer for me if you go.

Thank you for the suggestions. Dunblane hadn't been on my radar but certainly will take it into consideration. Regardless, the victims and all of those affected by that terrible event will be in our thoughts and prayers.

A second vote for Dunblane and its cathedral. I recently played in a clarinet choir concert there as our Scottish Clarinet Choir rehearses in Dunblane and I can say it's a wonderful building with very friendly guides. The town of Dunblane is very pleasant for a wander by the river and it's very close to Stirling, so could easily be combined with a visit there.

An update to the above. I'm not sure but the Renfrew ferry has probably ceased running this week.
On Thursday the new Renfrew Bridge opened- from Dock Street, Yoker to Meadowside Street, Renfrew.
It is the first opening bridge across the Clyde.
Dock Street is a very short walk from Yoker Station.