I agree with others who say it will create more difficulty by not inviting your son and ALL his family, and if they decline have a quiet word with your son and say you will all be disappointed if he can't join his birth family on this joyous occasion, so he might want to think about coming on his own.
I don't think anyone has thought to wonder why the DIL is so controlling. From personal experience I know that many mental illnesses (often undiagnosed) result in controlling behaviour as a means of coping with the illness. I have a close friend whose daughter has had an eating disorder for over 15 years and thankfully sought help, but the result was that she became controlling in all aspects of her life in order to also control the disorder. Fortunately, she was mature enough (and stable enough) to recognise that control of other people was not acceptable, and made great strides to rectify that - but it did take a lot of effort and counselling, and support from her mother. Fortunately too, she met and married a wonderful man who understood all this and is able to remind her gently and with lots of reassurance when she starts to slip down the same road again. Now she is leading a happy life and appreciates ALL her family, both birth and in-laws.
Perhaps your DIL has her own problems that she hasn't yet come to terms in.
But then, I am know for always looking for the good in people and sadly, sometimes get it wrong.
If your daughter is still adamant she doesn't want to invite her brother and his family I think the brother needs an explanation of why, and they he would be welcome on his own, but at the end of the day the decision is for your daughter to make - it is her special day, hopefully the best of her life, and nothing should be allowed to mar it.
I hope it all goods well.
Meg