Please don't be another person to trample all over your mum.
Moving forward, who will be the person who is going to be there for you when you arrange your wedding, have kids, and have hard times in the future? Is it your mum?
Does your dad help you out at all. Is he paying anything towards the wedding? Has he been there for you?
The adult thing to do is to invite him, and only him. If he declines, that is on him. Get your mum to walk you down the aisle.
It won't stop here. It'll be the wedding, then it will be your kids being told to call her Nanna, and come to the hospital, see the baby and be involved. As an adult you need to draw your boundaries with her now. She may be your dad's wife, but she (and him) took a wrecking ball to your family and your mum. He needs putting in his place too, which is not using threats of emotional blackmail to control how you feel.
As someone who in now in her 50's and put up with a selfish dad and putting a step mum and her kids before his own DC, I can tell you that I wished I had put him in his place years ago and cut him off, rather than do the "pick me" dance for 35 years. I am still waiting for him to put us first before her DC.