Something I get asked about a ton. Here’s what I personally like to do.
1. I do stick to her bed & nap times. I just do it more flexible, for example, right now her nap is 11:30a/12p to 1:30/2p, and she goes to bed at 8pm. So if we are traveling and we are having fun doing an outdoor activity and she is OK and can't take the nap until 1pm & sleeps until 3pm, then goes to bed at 9pm, I am OK with it! Whereas at home, I do always want her to sleep during the hours mentioned because I have appointments, meetings and work planned around her nap and sleep time, so it's more important for it to be "on time" at home.
2. If there is a time difference, but we are only gone for a week or less, I keep her on LA time. For example, when we go to Mexico and it's 1-2h time difference, she typically just wakes and goes to bed 1-2h later, which is fine with us because we get to "sleep in" a bit more, and we can enjoy the sunsets and go out for dinner with her. Keeping her on LA time mainly helps us get back on track to our routine super easy when we get back home.
3. If the trip is longer than a week, we eventually adapt to the local time, but it's something that happens naturally.
4. If the time difference is major like the 9h when we go to Barcelona, the change is so drastic I am not so worried about what time she sleeps, I follow her needs and just make sure she gets good rest to keep her immune system strong.
5. Other than naps + sleep times, we do try to keep the bed routine of dinner, bath, book and bed, but mainly because she needs a bath after being out all day. However, she is more tired on vacation because we are active and outdoors all day. Which means she does fall asleep quicker and harder when we travel, so the bed time routine is not as "needed" as it is at home.
So yes, I stick to a schedule but I'm not too crazy about it, vacation mode applies to this too! What do you do?