Major Adjustments to Travel Plans....Help!

I would suggest you need more time in Berner Oberland and Luzurn/Lucerne. Berner Oberland is a big area with lots to do, and weather can be an issue. I wouldn't stay in Grindelwald, we found it so touristy. I'd suggest Murren, Wengen or Lauterbrunnen, but that's a personal choice.

We thought Luzern/Lucerne was absolutely stunning and so much fun. We took one whole day just to take the boat trip across the lake, the cog wheel train to the top of Mt. Rigi. Then another whole day to explore the city.

I'm not sure what city I'd take the days from. I 've never been to Garmish, so I can't comment there. The rest of your cities are great cities, so again, its a difficult choice.

Note the correct spelling of Garmisch (-Partenkirchen) when looking online. I can't see any point in stopping for only a few hours in Munich, unless there is one thing you really want to see.
Note the train travel time from Garmisch to Grindelwald - over 8 hours with multiple changes. The whole day will be spent getting there.

I suspect with the kids you arent going to be doing a lot of highend museums on this trip? Of course I could be wrong. But if I am correct, then between that and the fact that the first night in Budapest is the night the plane lands, I would suggest you take a late train to Vienna. Maybe one that leaves about 4pm and you plan something good that morning in Budapest.

I know the train time will be long the day we go to Switzerland, but that's why I changed our plans to do Salzburg first. Am I correct in that taking less time to get to Grindelwald than Garmish? I feel like we'd be doing a lot of backtracking and dealing with train issues to go from Salzburg to Grindelwald. I do still have the option of staying with our original intenerary if that's not the case because I'm able to cancel all our lodging at no cost. Mr. E, with the morning we check out to leave for Vienna can we purchase train tickets the day of or do I need to purchase in advance. If we leave late that last day we'll have about 3 full days and some change for Budapest.

And thank you for the spelling of Garmisch- I've just been a bit stressed with learning of the construction on the train lines but have been looking it up correctly online.

Mr. E, with the morning we check out to leave for Vienna can we
purchase train tickets the day of or do I need to purchase in advance.
If we leave late that last day we'll have about 3 full days and some
change for Budapest.

The three full days will help. I just sent off a couple of tourists that spent 4.5 days here and its their 4th trip and they are upset they didnt plan for more time. Not all, but many, feel similar. An ideal stay is 4 days for most. I think and I think thats idea for Vienna too, if you love the museums. Without the museums or with fewer museums, 3 days is generally more than enough. Just one opinion, not necessarily true for all.

Here is an example buying tickets from MAV https://jegy.mav.hu/:

• Buy tonight for tomorrow Budapest to Vienna 16:30 to 17.20: 21 Euro + 2 Euro for a seat assignement.
• Same train in 3 weeks: 13 Euro + 2 Euro seat assignement.

Not terrible but 40 euro for your trip (about $50).

Same, using OBB for the tickets:

• Buy tonight for tomorrow Budapest to Vienna 16:30 to 17.20: 40 Euro + 3 Euro for a seat assignement.
• Same train in 3 weeks: 14.30 Euro + 3 Euro seat assignement.
  

Often not a good idea to buy tickets from OBB. For Vienna to Prague and Prague to Salzburg check with the Czech Rail Lines.

Mr. E, it sounds like we'll be buying early so I'll have to figure out timing. The cost increase in buying later makes a big difference with 5 people. And we won't be going to lots of museums so that makes it more feasible for 3 full days in each location.

Because the trip between Garmisch and Grindelwald is the longest, I would stop on the way for one day in Munich, visiting the Deutsches Museum for the kids.
https://www.deutsches-museum.de/en/

psa3011 if you need any help planning budapest, just let me know.