I know it's not okay for a dog to eat cat food, but can a cat eat dog food?

Cats are more complete carnivores than dogs. Dog food has too many carbs and not enough protein for cats to be healthy on. Most cats will snack from the dogs dish if there is something they like in there. If kitty is tubby try to increase her exercise level with active play sessions and watch her weight for six months. Cats lose weight very slowly. If that doesn't get her losing then you might have to go to a senior cat diet or a prescription diet which is very low in carbs. Also only feed her a measured amount each day. She may just have been overeating because she missed you. I 'm glad you two are back together again.