M.,
Congratulations on being the mother of twins. That obviously has many aspects that us mother's of singles never think about. However, the eating problem seems to be universally frustrating. It is hard. I have two events to share from my young mothering years.
First, I had a daughter who would hardly eat. Finally, I asked my chiropractor about it. He adjusted her and she began eating. She did not become a huge eater as a child, but immediately she began to eat more and enjoy it more. It seems that little adjustment relieved pressure on some part of her digestive tract.
My neighbor had a daughter who would balk at eating, so the mother let her down from the table and put her food in the fridge. If her daughter wanted to eat later, she got out the food that she had refused to eat. When she was hungry enough, she would eat. She learned to eat whatever her mother served. It worked for her.
Also, I have an extreme example of not finding a solution while the child is young. A few years ago, I worked with a teacher who had a little boy who would not eat. By the time he was in kindergarten, he had no interest in food at all and was feed with a feeding tube, even though he was capable of eating. In other words, this mom made an invalid out of her son because she did not keep at it till she found a solution. Don't give up.
I hope you can find something that works soon because part of this could become a behavior issue whereby he learns how to use it to control you. Remember that you are not only the kind and caring and loving mom, but you are the in charge mom.
Perhaps this does not describe you at all, but in today's society, children have often been put in such positions of privilege that they are not learning the safe and happy and wise ways of simple obedience which ultimately leads to a happier child and a more well functioning adult.