As other have said "It's their day, the start of their new family." He has expressed a wish for you not to be there, that may be hurtful and sad for you but he has the right to express his wishes, however, ...
What jumped out of your post was 1) your DD was shacking her head in the background and 2) he want's to be in control.
What is going on that your DD wants you with her when she is clear her OH does not want you there?
If at all possible I'd be having a talk with your DD when she is on her own (even if this is by phone) to clearly establish 1) what she wants in terms of support and 2) what does she understand by her OH's statement of "I want to be in control"
Me - and I accept it may just be me - but I'd be asking how controlling is her OH? In what situations is he controlling -if any?
Is he someone who really isn't in control of his emotions/actions yet feels the need to control situations/others? Or is he afraid that as much as he wants control he (like many of us) won't be able to be in control in such an emotional and unpredictable situation as a birth?
What is really driving his stated actions??? That's what I'd be trying to get clear information about and how does your DD feel about her OH's wishes over the birth and his actions around control generally.
There are a number of reasons people behave in this way, not all are unhealthy or unreasonable but some are and are indicators of future unhealthy behaviour.
I was very glad I was in the room for the birth of DGD. They had decided on a No Chemical Pain Relief Birth, all good stuff. I was there to use acupressure and relaxation techniques but as a Doula I could see my DD needed more help.
Midwife and Dr put forward a plan to SIL that wasn't too invasive and I could really see the reasoning behind it but he was digging his heels in on the No Pain Relief yet DD wanted change to go with the Dr's plan.
I was the lucky winner who got to talk him round. He'd had the we are trying to avoid a C section here and heartbeat/blood pressure talk from Dr.
DD kept saying I know what we'd agreed but I need this rest, that was then this is now. We got there in the end.
A couple of weeks after DGD was home SIL said "I don't know what happened, I don't know why I got to be that unreasonable, I'm sorry".
I did explain that as all their plans for a home birth went out the window he was desperately trying to hold on to comfort blanket of "the plan".
With all the changes and the fright of the situation his primitive brain had gone into the Fight, Flight, Freeze process and his rational brain was having a hard time getting back to working.
It happens, it happened to him then. He was just trying Freeze a changing situation fit into a fixed planned situation driven by fear but he was not going to let go of control. He's a good guy and a lovely Dad and OH but even he had a wobble.
So I'd be making sure you have a talk with your DD and listen to what she wants, why she wants it and why her OH wants 'control" and you out of the picture.
While I had to fight my DD corner and I know in the end the Dr's and Midwives will work with Dad to the point they have to ignore him because Mum and Baby's welfare really do come First.
Please take reassurance from the fact that if you can or if you can't work it out so that you are near your DD the Dr/Midwife will step in and make your DD and future DC's wellbeing more important that your SIL's wishes and if need be they will take "control".
However, you and your DD are still left to navigate the relationship part of the birth of your GC and the How and the What of the relationship with DD, SIL and DGC after the birth.
Is his wish to exclude you just around the birth of his and her child, the start of his own family? If so, it's understandable to a point so respect his wishes and manage the emotions as best you can.
If it's deeper and farer reaching make sure your DD knows even if she goes along with her OH for an easy life you are there when she needs to reach out. Don't push but don't move back. Good Luck with navigating your way through this.