"My research showed a place we can leave our backpacks at our near the train station..."
Good to hear - and news to my ears. Would you mind sharing that find?
"Traveling with kids is a whole different ballgame and I think we are going to be doing a lot of playing things by ear...I just wanted to know all my options"
Yes, very wise to play it by ear - but then you are making time-specific plans that commit your movements and reduce your options on Day 1 after a transatlantic flight. First off, your flight may be on time, or it may be delayed (happens quite often these days.) And if your family's like mine, jet-lag and drowsiness could be your travel mates. Kids and parents alike may have genuine trouble staying awake for the cruise that day. It seems you were thinking about this yourself back in May, when you had the cruise scheduled for Day 2, and when you wrote,
"We currently have 3 nights in Bacharach, the first being the day we arrive in Germany - I'm sure we will be a bit Jet Lagged."
Since you have shortened your Rhine stay - and since you want to enter the Rhine gorge by boat AND play it by ear - both wise choices - then I think you really should consider staying in Rüdesheim or Bingen rather than Bacharach. Then instead of having to get to Bacharach by boat that day (with your bags) you'd be able to assess where everyone is at after arrival in your town of choice - and make an informed decision whether to cruise either that first afternoon of the following morning. (Another good reason to cruise early in the morning might be the weather. No clue WHEN your trip is, but afternoon cruises in the warm months can get quite hot and uncomfortable.) If you wake up on Day 2 in Bingen or Rüdesheim and cruise north around 9-9:30, you could easily make a stopover in Bacharach to see the town for 1-2 hours.
Rick Steves' "one-size-fits-all" enthusiasm for Bacharach (attractive as it is) as a Rhine base town simply does not address everyone's needs. It's a nice town but really is more geriatric than family-oriented. As you discovered, there's a nice chairlift ride in Rüdesheim (among other diversions.) And Bingen has a fine facility for kids/families with a little free time - the Park am Mäuseturm, with water-playground, bike/skate park, and open grassy areas by the river:
https://www.bingen.de/media/be832181-1c59-418a-8f65-2d716b715341/r-h-ein-zum-spielen.jpg?mw=1200
https://www.bingen.de/media/d034d720-6a70-46b9-95f7-e060b66689ad/park-am-maeuseturm.jpg?mw=1200
We stayed at the NH Bingen hotel a few years back - very nice breakfast there in a dining area with expansive views of the river