<a lightbulb flashes on over my head> Maybe you could 'encourage' your DH to ride his 4-wheeler around the veggie patch on a regular basis. It might tear up the soil and compress the tree roots which would slow them down from invading your veggie garden area . . . a win-win??
Looks like a rather rural area. Do you have deer and rabbits around? You also may need a fence in that case or the critters will be the only ones enjoying the fruits of all those seedlings.
