It's difficult to predict how much time an individual traveler will need at a particular sight when she's not being lead around by a tour guide.
La Sagrada Familia: Are you going to ascend one of the towers? I did not do that. I did use the audio guide for the church, and I find doing that lengthens my stay just about anywhere. There's a small museum that (as I recall) focuses on how Guadi designed the building--the arches, etc. Many visitors seemed to skip it, but I did not. Then there's a very attractive shop. Honestly, I just don't know. I'm sure there's somewhere here braver than I am who'll be willing to make a suggestion.
Casa Mila and Casa Batllo I would put at a minimum of 90 minutes just walking around (both have audio guides). Casa Batllo tends to be super-crowded to the point that it may somewhat slow your progress through the building. Casa Mila is also very popular but perhaps not quite so mobbed. It has a potentially very time-consuming exhibition on the top floor, covering other Gaudi buildings. There are snippets of video, etc. I remember figuring that I spent perhaps 3 hours at Casa Mila, and I could have used more. I think it's fair to assume that I have a more-than-usual interest in modernista buildings. Both of these sites also have shops, with considerable similarity in their stock. I suspect (but confirm if this matters to you!) that one could return and visit the shops later if necessary, without paying another entry fee.
I recommend visiting Casa Batllo first, because I think your time there may be a bit more predictable. Be aware that even with a timed entry ticket (unless it's for the first time slot) you may be held up in line due to occupancy restrictions. Visitors are free to stay as long as they want. I'll really stick my neck out and say that a 2-1/2 hour gap between Casa Batllo and Casa Mila should be safe if you get the first entry time for Casa Batllo. You'll probably even have time to go to a nearby bar or café for a cold drink.
The walk from either of the Gaudi sites down to the Picasso Museum will take considerable time. Google Maps will estimate it for you. On the day I visited, the Picasso Museum was jammed like no other museum I've ever seen (I haven't been to the Vatican Museums lately). From online information I gather that my experience was pretty typical. It will probably take you extra time to fight through the crowds to get close enough to see the art. I do not recommend this museum for other than Picasso fans. Barcelona has other art museums where the viewing conditions are far better.