I think if they get either morning sun or afternoon sun, they should be okay. Usually 5-6 hours should be enough. Wouldn't it be easier to relocate the veggie garden to a sunnier location than take down a large tree? How about mixing your veggies in with your ornamental beds that get more sun?

I actually just planted a tomato in my front yard with the flowers.

You're right, I should just start a vegetable garden in the sun.

I probably will do that for the fall, but right now I've got this useless space on the side of my house, where there's about 9 feet between the house wall and the fence. I've had the compost bin there, and the soil is pretty good for planting. But it only gets sun 12-3:30.

Go ahead and mix up your veggies with your sun loving ornamentals this season. Plant something else ornamental that only needs part sun - hot afternoon sun at that in your new bed. It is surprising how good some of those vegetable plants will look with your ornamentals - especially peppers. You could even grow pole beans on ornamental towers if you have them or use inexpensive bamboo poles to build a tee-pee for support. I know a lady who always grows vegetables mixed in her flowerbeds in the front yard. She has even grown pumpkins and people compliment her on the lovely large green-leafed groundcover with the pretty yellow flowers! hee-hee!