Edinburgh to Stirling-Falkirk and Return in one day

If you have the means, I would suggest looking into hiring a private driver for the day. They could drop you off at each site and you could self-guide, then meet up and go on to the next town. This would save you a lot of time and hassle, and allow you to see all of the sites in one busy day. The RS Scotland guide lists private drivers, and has a self-guided tour of Stirling Castle (which I found to be excellent during my visit there this past September). If you also plan to go to Edinburgh Castle (EC) on another day, I suggest that you purchase the Historic Scotland Explorer Pass, which will allow you to skip the queue at EC.

I'll second both of Robert's suggestions. You ask if it is possible to visit all of your proposed sites in one day, and I hesitated to answer because yes it's possible, but would it be enjoyable? No, probably not.

At Edinburgh Castle the line for tickets could be 15 minutes, or it could be 45 minutes, hence the value of buying the pass ahead of time.

Unless you are just checking off boxes , this is too much , logistically , for one day . There is a great deal to see at Stirling Castle , The recently renovated Renaissance Palace ( with the marvelous Unicorn Tapestries , and Stirling Heads ) should consume more than a passing glance , as well as the regimental museum . You could manage Bannockburn on that day , but The Kelpies and The Wheel would be a stretch .

We did Falkirk wheel as a day trip from Stirling. We took a taxi from the train to the wheel and then the bus back to the train station. The taxi cost only slightly higher than the bus, so if I were doing this again, I would take a taxi both ways.

Stirling Castle is worth several hours. I enjoyed it much more than Edinburgh Castle.

Having just returned from Edinburgh a week ago, I ‘ll chime in.

We used public transport entire visit.

However I have a suggestion for you.
Take a look at the various tours Rabbie’s offers. Perhaps booking two distinct day tours is an option? That’s what we did.
We booked two separate day trips from their Edinburgh franchise, and loved it. Was cheap, and leaving the drive to an expert allowed us to relax and visit many sites without having to deal with any complexities.

Neither Rabbies or Heart of Scotland ('Wee Red Bus') day tours would cover all of Jon's desired places to visit in one trip. When I was in Edinburgh this past September, I took the Heart of Scotland day tour to Stirling Castle, the Trossachs/Loch Lomond, and Glengoyne Distillery. I highly recommend it, but it only covered the Stirling Castle part of Jon's proposed day trip. We had about 2 hours at the castle to explore on our own. That allowed us to go through the entire castle at a less-than-rushed pace, but no time to get to Bannockburn. We also drove by the Kelpies but did not stop. With that said, since all of the sites that Jon wants to visit are fairly close distance-wise, a private driver with car option would be the quickest and least stressful way to get from place to place in what would be a long, but I would think doable, day. Jon might even have time to stop at the William Wallace Memorial WWM), which is about a mile from Stirling Castle in the opposite direction from Bannockburn. If that would be of interest, I would suggest going to the WWM first from Edinburgh, then visit Stirling Castle, and then drive to the Bannockburn Visitor Center. I think a total of 5 hours in the Stirling area would suffice. After Stirling, I'd go to Falkirk and then on to the Kelpies on the way back to Edinburgh. If it is dark by the time you reach the Kelpies, I heard that they are amazing to see at night.