Last minute itinerary advice for family of 6

With only 5 nights available, I would strongly recommend you just stay put in Barcelona for the entirety and fly home from there. You simply would not have enough time to squeeze in another city. Also consider Easter Monday (13.4) is a public holiday in Spain you you may encounter some closures of shops and restaurants, but not so much tourist sites. with 5 nights you could also add 1 day trip your your itinerary. Some of my recommendations:

Kid friendly activities for Barcelona: Tibidabo Amusement Park (oldest in Spain), CosmoCaixa, Barcelona Aquarium, Maritime Museum, Parque del Laberinto, Rocambolesc (unique ice cream shop), Parque Guell, La Boqueria Market

Kid friendly daytrips from Barcelona: Montserrat Easy Hiking, Vall de Núria (Pyrenees), Tarragona (cool Roman Ruins), Dali Museum (I think they'll get a kick out of it), PortAventura (largest theme park in Spain)

It looks like you have 5, or perhaps 6, days. One of which will be used to travel to Spain and another to leave. I would spend the whole time in Barcelona, perhaps taking a day-trip. There is a lot to see in Barcelona and it has a great variety of sights, with things likely to appeal to children of varying ages.

Also Barcelona is more likely to have direct trans-Atlantic flights than most other Spanish cities (Madrid would be the other one that does), although I don't know if Delta use it. An alternative would be to split your visit between Barcelona and Madrid, but personally I'd stick to just the former and try not to spread yourself too thinly.

Whilst it's true that Spain's best cities are in the south, I don't think logistics make visiting them practical in the short time available to you - unless you can fly from Marseille to Sevilla, then catch a train to Madrid for the flight home (or fly indirect, via London for example). But even that is more hassle than I'd want, and Sevilla accommodation is expensive at Easter.

Thanks for the quick advice! In what part of Barcelona do you recommend that we look for accommodations?

I wouldn't split the time between two bases. You'll only have four full days, so I think it would be shame to spend time checking in and out of two different hotels. I believe you'll find plenty to do in and around Barcelona. However, we're talking about Good Friday here. There may be a lot of people on the move, so I don't know what the ticket situation is like for that train (which takes 4 hr. 32 min.). Barcelona is normally an extremely popular destination. I don't know to what degree that will be different around Easter this year.

Another possibility would be flying to Seville. Early April is, weather-wise, a great time of year to be in Andalucía. Normally, one needs to make lodging arrangements way in advance, but things may be a bit looser this year. Even so, I assume hotel rates would still be inflated.

I haven't researched the coronavirus situation in the various parts of Spain.

A third possibility is to spend all the time in southern France. What you have laid out gives you only two full days in Provence, which is extremely short.

Regarding COVID-19 in Spain, we have seen less cases than France, by a few hundred; we are almost on-par with Germany (slightly less). Number of fatalities is about the same as to the USA. So far, our current government has been hesitant to impose large scale quarantine measures or cancellations of mass gatherings, like one sees in France and Italy.

PS I meant to add that the Marseille to Barcelona express train, makes a few other stops in southern France. So, depending on where you are in Provence, it may be that another station is more convenient and the journey a little shorter.

I am so sorry that your family travel plans have been disrupted and uncertainty introduced. I hope you can gain some clarity around your decision making, and travel if possible without fear or apprehension.
I would think about a 4th night in Provence followed by another 4 nights in Barcelona. I wonder what your plans are for Provence? Avignon, Arles, St Remy, Nimes, Pont du Gard ??

You wrote:
"In what part of Barcelona do you recommend that we look for accommodations?"

We stayed across from the Cathedral at the Hotel Colon (Barri Gotic quarter), but I've also seen the Eixample area recommended in this forum. .And I found this recent post:

https://community.ricksteves.com/travel-forum/spain-reviews/hotels-in-barcelona-57150e48-8fbe-4668-8867-d29bcf860af5

If it rains take the family to the Maritime Museum. Even if they don't like boats the galley is impressive.

Thank you for your input.

I'm terribly sad to report that we decided last night to cancel/postpone this trip. We're going to be out almost two weeks worth of the cost of accommodations. :(