i think you want to think about 2 things:
*not something sweet because you already have 2 sweet mains
* texture- not something soft because you alrdy have that with the corn dish.

Unsweetened green beans or sauteed greens would be my choice. Flavors of both would work.
As to greens, i think spinach and swiss chard are too soft for this menu, and I prefer sauteed kale to collards myself, but that's up to you.

A cabbage slaw/salad is a nice crisp addition to ham and corn pudding.
Make it 'angel hair cut' and dress it with either a lime/olive oil dressing. Or a creamy base dressing that's a mix of Italian vinaigrette, some tomato paste/or ketchup and sugar, and a creamy element like mayo or yogurt.

Desert: Banana pudding or oatmeal cookies.

I'd also go with the collards - or some other kind of greens - braised with a hamhock, or bacon, or something piggy. Alternately, green beans, treated similarly, maybe with some tomato thrown in - you could do a more 'modern' crisp version, but with that menu, I'd go for green beans your grandmother would love. A little something pickled would be a good counterpoint to the richness too.

Asparagus would be nice. You could marinate it in a sharp vinaigrette--not too strong as to detract from the flavor of the asparagus--and for a pretty presentation serve it with marinated halved red and yellow grape tomatoes spilled over the the top.

Well, I'd probably do collards with that menu. You can't go wrong there. :)

Grits. Red beans and rice. OKRA! (not Oprah). Of course I'm one of those cooks who doesn't need to see a salad arranged around every meal.

peas with mint and butter, broccoli salad, zucchini ribbons with parsley pesto, green beans with dill, tomato salad a green slaad with strawberries, pecans and goat cheese