How to do the first 5 days of the 21day tour on my own

The easy way to plan your trip is to use this service--https://www.ricksteves.com/travel-help/plan-your-trip-with-our-expert-consultants

Here is an alternative--https://www.ricksteves.com/travel-tips/transportation

If you are starting in Amsterdam, you might wish to stop in Cologne for one night to see the Cathedral.

Then proceeded down the Rhine. Rudesheim is a great wine area to visit. Rothenburg on the Tauber is a considerable distance from these places. I would look for a tour of The Romantic Road that ends in Munich. If you can't find one, there should be tours from Frankfurt.

You can easily move between Amsterdam, Bacharach and Rothenburg by train. Check the Deutsche Bahn website for schedules. The day cruise on the Rhine is easy - take the train from Bacharach to St. Goar, tour Rheinfels Castle and then take the boat back to Bacharach (the "Rhine cruise" mentioned in the tour itinerary). The day 3 itinerary could be tricky using just public transit, so maybe replace it with a stop in Cologne as previously suggested. Amsterdam to Bacharach trains generally require a change in Cologne, so it's along your way. My observations are based on having taken the Best of Europe tour, but days 1-5 of the Family Tour appear to be very similar.

Travelling on your own using public transport is slower than an organised tours with a coach and driver on call.

Day
1. Travel Amsterdam to Koblenz
... either via Cologne
... or Brussels & Luxembourg
2. Day trip on Rhine - KD Line
3. Travel to Wurzburg (direct trains)
4. Day trip to Rothenburg ob der Tauber
5. Travel to Munich (direct trains)

I visited Rothenburg on the train from Frankfurt several years ago and the train did not go all the way to Rothenburg. I had to catch a bus which slowed down my arrival. Perhaps it has changed.

"I would like to follow the first 5 days of the 21 day tour... Anyway how would I coordinate starting in Amsterdam, taking a day cruise on the Rhine and visiting Rothenburg."

Hmm... Rick's bus tour rushes through these 3 places because it's a 21-day tour with so much in it. He has only one day (#2) for A'dam. He visits an open-air museum near Arnhem on Day 3 (this would likely be too time consuming and tricky for you independently) and then spends the rest of the day getting to and staying in Bacharach. The Rhine visit is similarly rushed; the cruise he takes hits only half of the best scenery.

If you have only 5 days, you may not want to replicate his itinerary exactly. Will you be landing in A'dam after an international flight on Day 1? That circumstance means sightseeing will probably be very limited as it's mostly an adjustment day. If your time is equally short, I suggest skipping Amsterdam altogether. There's too much ground travel and too much shortchanging of destinations on top of A'dam as well. I would suggest...

• ...flying into Frankfurt and moving immediately to the Rhine (2 nights.) Take time to see Marksburg Castle or Burg Eltz as well - these are intact medieval castles. Rick's lightning-speed tour only takes you to Rheinfels Castle ruins (it's worth visiting but NOT the same at all) even though he says Burg Eltz is his favorite castle in all of Europe!

• ...Day 3, Morning and lunch on the Rhine; afternoon train trip to Würzburg, as David suggests (1 night)

• ... Day 4, full day in Würzburg - view from the fortress across the town - some great things to see here, including the UNESCO World Heritage Residenz Palace - take a tour; evening train to Rothenburg (2 nights)

• ..Day 5, half day in Rothenburg, half day by train at Bad Windsheim's open-air museum (this one is very good and pretty easy to do on your own,) return to Rothenburg for the night.

There's been a train to Rothenburg for as long as I can remember. There'll be one there when you go too. The previous poster might have chosen to take the Romantic Road bus instead. OR, it's possible there were track repairs underway, and DB provided replacement buses (Ersatzverkehr)