I think you have pepper plants in that last picture. They look pretty nice, but are much too close together. I'd advise you to thin out to about a foot apart, and transplant the ones in between to another row or somewhere else. (pots in the sun preferably)
The tree in your neighbor's yard shows up in your first picture, and it is huge! Don't forget the issue with trees isn't just the shade they throw, it's that their roots are under the soil everywhere, out past where the branches reach, so they will invade any plantings you make within their perimeter.
Any way you could cut back a couple of branches of the pine tree to give your veggie plot some more sun? Filtered shade just isn't enough. They need direct sun.
