I went to Sicily for 2 weeks pre-covid with DH- no kids. We started and ended in Palermo though, but did go to Catania. We caught a coach from Catania to Syracuse for the day. Walked around, saw the shops and sights, had a stunning seaside lunch and really enjoyed it as a day trip. Italians seems to love children- so you will be ok. 🙂
Taormina was another day option, which I really wanted to go to, but Mt Etna was grumbling and I'd read it was pricy. Likely more so if staying there though, rather than just as a day trip.
Like most of Italy, Catania has an amazing fruit/veg market. Also a seafood market where swordfish (spada) seemed to be everywhere. Complete with being skinned/gutted on the street.
If you enjoy trying local foods, you will see horse meat on the menu! Something I'd only seen in France before. Clearly not for everyone, but might be worth mentioning to DD beforehand, that on English menus, she might see this as an option.
I visited off season to avoid the heat, so not the peak of summer. There is an ice cream in a bun (or vaguely similar?) which I was told about, but not on sale when I was here. Apparently that is nice, but I can't say either way.
One thing to check is what will be open in August? I thought majority of Italy was on holiday the entire month, so you 'might' find museums, touristy things, cafes etc all shut. Maybe not, but check beforehand and have a fabulous time.