Step family won’t go to my wedding because I’m not inviting their kids

Generally when people invite only "some" children it tends to only be received well by guests if those children are invited solely because they are part of the bridal party, or, because they are the couple's children.

I personally can understand your step mother's feelings here because she may see it as a snub that you're allowing your bridesmaid to bring her daughter but her grandchildren aren't invited.

If your bridesmaid's daughter is invited solely because she is in the bridal party, then it may be easier explaining this to your step mother that it is only those children in the bridal party who are being invited. If not, it'll be harder to diffuse the situation and you may have to accept that they simply won't attend.

Personally I don't know why anyone would want to bring their children to a wedding but there definitely are those people who take it to heart if their children are not invited.

They’re overreacting. The answer you need is “sorry to hear that. You’ll be missed.” Don’t cave in.

Agree 100% - I'm stealing this response when my FH's grandparents threaten not to come when we don't invite my FH's half brother (who is toxic and ruins everything for my FH) and his family.

Your stepmom is wrong.

They are definitely overreacting. If they care about you so much then why are they giving you an ultimatum. They're making the wedding about them instead of what you want. I think the only time family should get a say is if they are financially contributing.