We spent Christmas in Seville years ago pre kids, and it was great. Warm enough that you could just take a light coat and sometimes sit outside without wearing a coat at all. Not hot obviously, but it was great to go from miserable gloomy UK to (almost always) sunny Seville.
We stayed in an apartment in the city centre and there was loads to do in Seville. I should think your 3 yr old would enjoy the Real Alcazar, which is fantastic for adults too. Mostly it didn't feel hugely Christmassy, I think because it was just so different from being at home, although the apartment-owners had put up a tree and decorations. But the shops were beautifully decorated with Christmas lights and things.
It was no more expensive than other times of the year - the price for the flat we rented was basically one price all year round and then a higher price for their peak season which is Semana Santa and some other week in the spring I've forgotten the name of. Ooh, and the flat we rented had a rooftop jacuzzi, which we used every day! Perfect and would work brilliantly for you once the kids are in bed. (I'm not on commission, honestly! Here's the link to the flat we had, in case you're interested www.sanandresapartment.com/ )
We flew with a budget airline and I don't remember it being particularly expensive - we did book quite a while in advance though.
And if your kids are only 1 and 3, I'd guess they're not so big on the Christmas trimmings yet?! Mine weren't at that age. As long as Santa came, I don't think they'd have cared about any other Christmas trappings.
Go for it! Have a fabulous time wherever you decide to go.