Linderhof and Neuschwanstein Castles on the same day?

First of all do NOT waste a Rail Pass on this journey. All 3 of you can travel all day long all over Bavaria (including Munich, Linderhof, Fuessen) for 33 Euros.

I almost always recommend taking public transport. But if you want to easily see Linderhof and Neuschwanstein in 1 day the easiest and fastest choice is to have a rental vehicle. it's about 2.5 hours from Munich to Linderhof via public transport. The journey from Linderhof to Neuschwanstein ranges from 2:10 to almost 5 hours. It's really a super long day mostly spent on public transport. It's up to you of course to make that decision.

But don't waste your money on a railpass. The only country where railpasses come in useful is Switzerland with their super expensive prices some sort of a Swiss Rail Pass usually comes in handy.

Another thing to consider, I spent almost an entire day at Linderhof. The palace itself is small and the tour does not take very long, but the grounds are extensive, with many photo ops.There is the fountain in front, a couple of "out-palaces", the Grotto. And I was there long enough that I had lunch at the restaurant at the entrance half way through.

You can only stay inside Neuschwanstein for the tour; that takes about 40 minutes, but the walk up to the castle and back down takes over an hour.

If it were I, I'd come down on the train to Oberammergau with a Bayern-Ticket, check into a hotel near the station (here's one), and go out to Linderhof. Come back, see some of Oberammergau and spend the night. In the morning, buy another Bayern-Ticket and take the bus (included with the Bayern-Ticket) to Hohenschwangau, tour both castle, and see a little bit of Füssen. Then take the train back to Munich in the evening.

I agree with Lee. The actual palace of Linderhof is only a small portion of the total attraction. The grounds are extensive and the whole things takes at least three hours to explore.

PS- Pre-read about Ludwig II's weird fascination with Wagner and his operas and all of this stuff will make more sense.

My question on the Bayern ticket is I thought I read it is only good Monday-Friday and we were planning to travel to the castle(s) on Saturday. Is that right?? Maybe I need to rearrange my visit to Bavaria so it is on a weekday?

"My question on the Bayern ticket is I thought I read it is only good Monday-Friday"

No, it's good every day. On weekdays, it's only valid after 9 AM, so if you need to start earlier, you can buy a separate ticket to cover you until then. (For instance, if you're starting at 8:45 AM, you only need to buy a ticket to get you to the first stop you will be at after 9 AM; then your Bayern Ticket kicks in). On weekends, it's good all day. It is only good for the day stated on it; the default is that it's valid for the same date you buy it, so if you're buying in advance, be sure to get it for the right date.

Also agree with Lee. I've found all three castles [Linderhof, Neuschwanstein, and Hohenschwangau] worth seeing in different ways, and spending a night in Oberammergau would be ideal in between them. We've done the hike from Schluxen (in Pinswang, between Füssen and Reutte) to the latter two castles several times and really enjoyed, but that might be too much to cram in.