Critique my Barcelona itinerary

[WalkWithMeSuzieLee]

Off to Barcelona in a couple of weeks - 2 adults, 2 DC aged 11 & 8. Don't want to miss any highlights and I know some places are best booked in advance, but also wary of overscheduling, wearing us out and not having time to just wander/play. I have unpredictable mobility issues also - so planning a mix of walking, public transport and taxis if need be.

Our flight is due to land Tuesday afternoon and we will be leaving Friday afternoon to catch a train down to Sitges for a few days on the beach. We're staying in the gothic quarter close to the cathedral. How does this sound? Too much, too little? Have we missed any must-sees or is there anything you wouldn't bother with?

TUE EVENING
Barceloneta beach so the kids can play/paddle, and find a restaurant nearby.

WEDNESDAY
Casa Batllo first thing then I've found a great looking brunch spot nearby.
Park Güell in the afternoon with a picnic dinner. Unsure whether to also book the Gaudi Experienca (4D thing).

THURSDAY
Tibidabo or Montjuïc (which is better - obvs M has several museums etc but is T more fun for the kids? It's a bit of a schlep though) in the morning/ early afternoon, taking a picnic with us.
Early dinner in a restaurant near our hotel then a short walk to Park Ciutadella followed by the Picasso museum (which I understand should be free from 7-9 that evening).

FRIDAY
Sagrada Familia in the morning followed by lunch at a nearby tapas bar.

I think your kids would enjoy the cable car ride over the harbor up to Mont Juic.
Park Guell and Sagrada Familia are in the same area so might be better to do them on the same day.

Thank you, yes that makes sense actually, I'll swap Casa Batllo and Sagrada Familia.

Cable car sounds fun. I assume most of the Montjuïc attractions don't need prebooking? Would rather see what we fancy doing when we get there rather than rush about between museums.

I wouldn't bother with Tibidabo, it was admittedly many years ago that I went but a real trek to get there, very expensive attractions and not that many of them so you'll have exhausted it quickly. The best thing about my visit was when the ice cream vending machine took my money without delivering my magnum, so I walloped it and it spat out three. Total win!

So I agree with PP that Montjuic is probably a better bet, combined with the cable car it's an all round nice thing to do with kids. Also if you like swimming, the municipal pool up there is absolutely glorious. Just a big pool (no slides) but it's perched on the side of the hill with a panoramic view of the city and sea. Big pool with plenty of room for kids to play and very relaxed - not for serious lane swimming so conversely great for chilling. And because it's the municipal pool, not pricey at all!

Port Aventura (and Ferrari Land and Costa Caribe) in Salou are only an hour away from Barcelona by train and well worth it for a day trip that the kids won't soon forget!

I would just say that we found when we were in Madrid that the top art museums, the Prado and the Reina Sofia, had the most epic queues to enter during the free 2 hours at the end of the day, people were literally queing for what seemed like miles around the block. We actually paid to enter, but could see the hoardes queing when we exited. The kids are probably free to enter anyway, so I would consider paying and going in earlier in the day. Also early dinners are not very Spanish, they usually eat at like 8:30/9 or later even with kids. Probably some open all day type places where you could eat at 5:30 if you needed to.