I'm sorry that your husband was disappointed and rejected by his parents. I'm sure that was very hurtful, and it left a scar on his psyche.
But I think it's a shame that he would insist on inflicting that same rejection on his own daughter, to make sure that she is as held back as he was. Don't we usually want more for our children than we had? We try to make the best of what happened to us, and do just a little better for our own kids.
Your parents live with you, so they must be particularly close to your daughter. So you have given them this gift of housing and family closeness, yet your husband will prevent them from repaying that by giving something to your daughter in a time when college expenses are exponentially higher than they were when he was her age? Is he also going to reject scholarships that are based on her achievement and character? I'm guessing he will not. But he wants to prevent people who love her from endorsing her pursuit of higher education, from investing in the many contributions they hope she will make to this world when she graduates with a good education. He's letting his own ego and his own pain play out in the life of his daughter because...why?... he thinks this is an insult to his own earning power? What a shame.
Let them pay $2000 toward her tuition, or have them apply it to her books and living expenses at college. I think it's doesn't make sense to give it directly to her - kids may spend it rather than save it. That's probably why your parents said it's $1000 if they give it to her, and $2000 if it goes toward college.
If your husband still refuses, I think your parents can independently decide to give your daughter a gift, perhaps in a monthly or quarterly installment directly to the college, or directly to her, to underwrite her expenses, her "luxuries" (like going to campus concerts or buying school name sweatshirts and so on, stuff every kid wants). Those are expenses you would probably wind up paying, so let this be their gift to her. Paying the college directly means they would give a bigger gift, right? I'd choose that.