Is Day 1 an arrival-from-US/Canada day? If so, I don't know that you'll be in condition to appreciate La Sagrada Familia.
Day 2 is very packed. The mandatory PdlMC tour takes about an hour. The other sites are probably more like 90 minutes, not including travel time. La Pedrera can be 3 hours if you want to spend time on the top floor, looking at the (quite interesting) information and videos about Gaudi's other sites. Casa Amatller (tour required) has a pseudo-castle rather than a modernista interior; not sure how much that will interest you. I think it's going to be pretty scary buying so many timed entry tickets for one day. Those tickets are mostly 20 euros or more. How will you feel if you have to rush through those sites to keep to your schedule? I'm also wondering whether you will have time to eat. PdlMC could instead be done on Day 3 (unless it's closed?), which would help a bit.
Day 3: I haven't been to Parc Cituadella; it may be lovely. But I think it would be a shame not to spend some time seeing the Barri Gotic and other medieval sections of the city. You can expect the Picasso Museum to be absolutely mobbed to the point that you spend extra time there trying to get close enough to the pictures to see them; I don't recommend it for people who are not true Picasso fans.
Day 4: MNAC is quite large. I sort of rushed through a lot of the rooms of paintings and still spent 5 hours there over the course of 2 visits. The modernista collection is very good, and the church frescoes are amazing. Those are things you can't see many other places.
Although I enjoyed Palau Guell and Casa Amatller, I'd swap one of them for the Sant Pau modernista site. That's assuming you don't crash and burn before the end of your visit. From my perspective you've made really good selections, but it's a lot for 3-1/2 days. Or 4 days. Or 5 days.
I believe some of the modernista sites are open past 5 or 6 PM. That might help. It's not like you can eat dinner early in Barcelona, anyway.
In my experience last August, tickets could be bought 2 days (in some cases 1 day) ahead of time, but 1) I might have been lucky; and 2) my schedule was not nearly so tight, so it wasn't like trying to fit a jigsaw puzzle together. If you want to ascend a tower at La Sagrada Familia, that's an extra timed entry to be coordinated, so LSF might be the first one to book. Someone here suggested an hour after the church entry time, which is logical, but leave a bit of extra time after the tower, in case you haven't seen all of the church and the small museum before you need to line up for the tower.
