Would a tree make that much of a difference?

Hi, we garden on the western slope of the Sierra Nevada's and have a large willow tree on the East side of the garden. The beds that are closest to the tree (about 20' to the west) are planted in melons this year and we noticed that those melon plants are very stunted, while the beds farther away are doing fine. Yesterday I watched the beds and the most stunted bed (closest to the willow) doesn't get sun until

11am. Our sun sets around 8pm right now (up to 9 during the longest days in June) so these plants do get 8 hours of sunlight. After 11 it gets really really hot and doesn't cool off until evening. I started to think that maybe the melons might shut down during the hottest part of the day, and since they missed all of that morning sun, that might be what's stunting them. Also, could the roots of the willow be sending something toxic? I have done soil test and come up with 6.pHs. We use lots of chicken and horse compost. We had soft rock phosphate every year (our soils are deficient in that product). Last year I grew beans in the same spot and they did great. Thanks for your time. Janet

Thanks everyone so much for your response. The melons were so stunted, I pulled them out and dug up 2 of the beds. No roots, so it must be the shade. I have replanted with lettuce, beets and spinach. The lettuce beds we cover in shade cloth by using concrete mess and bending it into hoops and covering that with shade cloth. Next summer I'll plant crops in that spot that do not get stressed by the sun. Again, thanks, Janet