Need help with scheduling a day trip to Sintra

I would actually suggest going up the hill on the bus as early as you can,
as the Pena and Moorish are both up there, and you will suffer the crowds
to get to either one. It's walkable between the two, so you might as well
see them both, then take the bus back down. Moorish will not take that
long IMO.

If you take a break after that, you still have the whole/most of the afternoon
to see the other two places. It's walkable (although a bit of a stroll) to Quinta
de Regaleria, but if you're pressed for time, I'd take the bus to both places
and time my schedule based on the bus schedule.

Sintra visit questions and answers are frequent and plentiful on this forum.

If you scroll down few weeks/months, you will get plenty of first-hand experience and advice.

Here is one suggestion (different people have different viewpoints)

1. Uber/Bolt direct from your Lisbon hotel to entrance of Pena (this is very good use of your money compared to going to train station, wait for train, take train to Sintra, struggle with bus or other transport)

2. You do not need timed ticket to visit the beautiful castle and terraces. You only need ticket if you want to see the inside of residential place (meh IMHO).
   So untimed grounds only ticket is perfectly fine.

3. Monitor Sintra weather. It could be very different than Lisbon weather. Grounds tickets are unlikely to sell out so that you can buy online previous night after checking weather.

4. Recommend buying 3 euro add on for the green bus that takes you up the steep hill from Pena Park entrance to the castle. That's great help in saving your time and energy. One tip: bus is small and gets full. In that case volunteer to stand as bus ride is less than 5 minutes.

5. After Pena, one can walk over to Moorish castle but IMHO there are better places to spend your precious energy and time and it is so much easier to get Bolt from the entrance of Pena rather than Moorish Castle because of one way nature of the long circular road

6. Take 4-5 euro Bolt/Uber to Regaleria. They will try to drop you at bottom entrance where taxi stand is
   But that is actually exit. Entrance is up the steep hill. So ask driver to drop you at the upper ticket entrance

Rest of the day can be spent in multiple ways
1. Uber/Bolt or local bus to/from Monserrate
Or
2. Stroll through Sintra Old Town
Or
3. Take Uber/Bolt to Cabo, privately ask him to wait for 20 min and take you to Cascais with another 15 min stop at Boca. Dinner at Cascais before taking train or Bolt back to Lisbon.

Thank you to you both for all the detailed info for Sintra. I was concerned about the logistics of visiting, but I feel that now I have a better handle on it.
Best wishes,
Kathy