i am worried about a tree in my veggie patch

Yes, the tree will take water and nutrients when feeding itself, also rob your vegs. of light. It is best to have it taken out, or do not plant underneath it's spread.

You might also encourage suckers to grow when you dig around it. I'd try to remove it and then improve the soil for best results.

If you cannot move the tree - then the only other answer is to build up raised beds. Nearest to the tree i would put mypex or some kind of membrane - to stop the roots or suckers coming up into your fertile beds. Make beds 4ft wide and as long as you wish and at least a foot high. then add compost, soil, anything to build up the soil height and improve the fertitity, then plant your veggies and mulch well!