You are trying to cram three or even four days' worth of sights into two days. It's going to be exhausting, and possibly stressful due to scheduling issues.
I'm concerned that you say you "were planning on" the Picasso Museum and the Palau de la Musica Catalana on Day 2. Want to be sure you're aware that you are required to take a tour of the Palau (English readily available) so should pre-book. Your time in Barcelona is extremely short, so you don't want to have to wait around for hours until there's an opening. The lines at the Picasso Museum can be incredibly long, so you should arrange that in advance as well. Time needed in the Picasso Museum may be longer than expected due to the monumental crowds; it's difficult to get close enough to read the labels posted near the paintings. On the other hand, the conditions might send you lurching toward the exit after an unexpectedly short time. I have no hesitancy in recommending that you skip the Picasso Museum unless you are a fan. I'd be inclined to book the Palau first, since that is a more predictable visit, time-wise. If you have a bit of time before the Picasso or any amount of time afterward, wandering around the Barri Gotic is good if the Sandemans Tour doesn't cover it.
Your Day 3 is going to be an extremely full one. I'd figure on at least 1-1/2 hours at each of those sights, plus travel time between them. You'll need to pre-purchase tickets for all of those places to avoid lines that can extend to an hour or more. There are safety-related capacity limits at Casa Mila and Casa Batllo, so you may still have to wait outside for a little while, even with a pre-purchased, timed ticket. So you need to pad your schedule a bit--but by how much? Also, at some point you will need food. I believe Casa Mila and/or Casa Batllo offers a higher-priced wildcard ticket that allows you to just show up at a time of your choice. That would be a good strategy. Even so, you face significant scheduling challenges. You might do better to settle for either Casa Batllo or Casa Mila. In my one experience (2016), they were both very busy, but Casa Batllo was more packed. It didn't affect ones ability to see the building interior, but it made Casa Mila a bit more pleasant for me. You could Google for photos to see if one of them grabs you more. If you are determined to see both, consider an evening entry time for one of them. I believe those sites are both open late.
