Travel from Seville to Granada via Cordoba - large group with kids

Is your plan to travel to Cordoba for a day visit then on to Granada all on the 13th....as well as arrive in time to see the Alhambra on the the 13th?...or is there a misprint that you will travel on the 12th?
There are 'car hire plus driver' but whether they have a vehicle that size is another matter. You also will need to determine whether a private driver is considered a 'taxi' or not as a rental vehicle requires car seats and taxis are exempt. Also, if you are having them wait while you visit Cordoba, it might bring the pricing close to the rental cost.

I find buses quite easy to use when I have a suitcase that's larger than carry-on size. You don't have to wrestle the bag up onto the bus; you just roll it to the side of the bus and lift it into the hold. Buses normally stop about every 2 hours for a rest break, but I can see how that might be a long time for young children.

The travel leg from Seville to Cordoba would be much, much faster by train than by any other means. You would, however, have to get those bags onto the train, along with the two children.

Sorry for the typo - I meant we will do Seville to granada via cordoba on 12th May and see the alhambra on 13th.

Checked out private transfers and they seem to be way way expensive. The only option left is to take the bus/train to cordoba, drop the luggage at the lockers at cordoba stop, see the city and take a but to granada.

We might just skip cordoba and head straight to granada and spend some time there.

As a stopover, is cordoba preferred over malaga. We like to see natural beauty, architecture etc. Not a fan of museums.

Malaga has a lot of museums of interest to me. Otherwise, for the typical tourist not looking for beaches, Cordoba ranks a lot higher than Malaga.

Might the children fall asleep on the bus to Cordoba after a busy day?

I took the bus from Granada to Seville and they stopped part way for a 30 minute rest stop - that made it 3 and a half hours. Not sure whether they stop Cordoba to Granada.
FYI, train is faster to Cordoba from Seville and across the street from the Bus station - which I believe is where the lockers are.
It is about a 15-20 minute walk to old town Cordoba from the stations. harder going back, because it is a bit uphill (but I had luggage). There is a promenade park down the main boulevards from the station to the old town. Part way along is the Mercado Victoria, which was the old food market, now a big food court. Cordoba doesn't have big endless museums (except perhaps the archeology museum). It has a delightful bridge with islands in the river - and different birds to look at.