Oh, I see.

I honestly disagree with this as someone who’s currently planning a wedding.

Let me ask you a question, then. Two, actually.

She should have to pay for their seats at her wedding if they don’t like her and don’t want to be there.

Do you honestly believe that everyone at the wedding you're planning like the bride or the groom?

The half siblings would only go to save face.

Do you honestly believe that nobody at the wedding you're planning are only going to save face?

If this was any other person, it would be no brainer. You don't invite people to you don't like or that don't like you to your wedding, that's easy. But these guys are family, regardless what the OP says, because they are going to be a part of OP's mother forever. They are going to see each other again.

Again, from where I come from, weddings are traditional affairs meant more for the family than for the bride. We often say here that, for your wedding, you first invite everyone you have to, then some of the people you actually like.

Anyways, I see your point. My point, however, is that weddings IMHO are social affairs with a inherent ammount of saving face for no reason other than looking pretty and I don't think it's such a terrible think to save some face for the sake of a loved one.