trip to Barcelona 4 day itinerary

We are arriving to Barcelona May 25th with a 9 yr old, 15, and 16 yr old.  We arrive mid day and will stay until the 28th.  From there we will be in the Costa Brava area until June 8th.  We can give or take days as we have not arranged places to stay yet.  While in Barcelona we put together an itinerary but I have no idea if this is too much in a day or reasonable.  We haven't chosen specific tours but would like shorter, kid friendly tours.  Would appreciate any recommendations and opinions with regard to our plans thus far.
May 25th (arrive around noon)
Settle in
Free walking tour for general info
Beach time
Spanish Tapas Tour
Flamenco Evening show/drink
May 26th
Breakfast at Mercat de la Boqueria
Gothic Quarter tour
Lunch and Museu de la Xocolata
Guidi tour/Sagrada Familia/La Padrera
See Arc de Triomf/Eis Quatre Gats
Evening: La Rambla/Placa de Catalunya/Placa Reial
May 27th
Day in Montserrat  hiking/bouldering/monastery
May 28th
Park Guell Tour
Beach/Lunch
Illusions Museum
Poble Espanyol
Later in day : Montjuic Castle/Funicular
Font Magica de Montjuic (night show)

Think you have it all pretty well covered but sounds exhausting.

Worth considering the Hop on Hop Off Bus Tours to get you around to some of these places.

Make sure you book ahead, online for Sagrada Familiar, normally long queues, allow plenty of time, it's magical.

If football fans, what about Camp Nou Tour.

Whetever you are, especially busy tourist places, beware of pickpockets.

Hope travel and tourist sites are all open again by the time you go, stay safe.

I think you should change your name to Mistic Meg ..as you seem to have a crystal ball that is telling you some news that the rest of us have been waiting for.. apparently Covid 19 has put a stop to any Tourist type Travel  right across the EU ..and I am pretty sure this includes Spain good luck anyway and don't forget to come back and tell us how you got on.

Exactly, windtalker. Considering some airlines say they won't even get back to a limited flight itinerary until the middle of June then I think planning a trip to one of hardest hit countries in Europe for that date may be a bit optimistic. And to one of the most hard hit regions as well. 

The Spanish government is only allowed to extend these alarm periods by two weeks at a time. Even the so-called easing of restrictions from yesterday still makes Spain's lockdown rules far more stringent than the UK one. Especially in one of the most hard hit regions in Spain at that which is saying it will ignore the government return to normality (if that is what it is) and impose even more restrictions. Doubt if restaurants and bars or possibly even hotels will be open at the end of May.

I think the OP plans are good but would definitely not count on them for May this year. 

The city of Barcelona is completely safe and there are no unsafe or dangerous areas (some areas in the old city might make some uncomfortable, even though they are safe).
Barcelona is also compact, walkable and has an excellent and inexpensive public transport system so you can also stay a bit off center without a problem.
The recommended central section is in the Eixample district in the southern half of "La dreta de l'Eixample" neighborhood or in in "L'Antiga Esquerra de l'Eixampl" neighborhood , in both between Pl. Catalunya and up to around Carrer Paris.
For quieter streets try Rambla de Catalunya (do not confuse this with Las Ramblas - which you should avoid) and Carrer d'Enric Granados. Sant Antoni is also a good and family friendly neighborhood, still central and well connected but less touristic.
For a bit off the center places you can look at places in Vila de Gràcia and Poble Sec, two lovely neighborhoods with lots of restaurants and great atmosphere (both can get a bit noisy in some parts, especially during the weekend, especially in Vila de Gràcia).
Once you have a few options you can ask for our opinion on the specific locations. When checking a location also check the public transport or barcelona taxi transfer options nearby.
Must do in Barcelona - the Gaudi houses are very interesting, the strange architecture seemed to interest my kids. They liked Casa Battlo (it had an interesting "audioguide" on an ipad that my kids - 7 and 10 at the time - liked) . Also Park Guell for similar reasons. 
Kid friendly activities for Barcelona: Tibidabo Amusement Park (oldest in Spain), Montserrat Hiking, Vall de Núria (Pyrenees), CosmoCaixa, Barcelona Aquarium, Maritime Museum, Parque del Laberinto. Make sure to try Rocambolesc, world's best ice cream shop, from Michelin Stared Roca Bros., they have locations in Girona and Barcelona.

Barcelona is my favorite city

Each to his own - I reckon it's over priced and Valencia has a lot more to offer.