I can see how your SIL's presumption that her friend is always welcome came about. That said, you, as hostess, decide on the meal, the entertainment, and the guest list. These are not just privileges of the hostess and host but the responsibility too.
Things change over time. Events change. People change. relationships change. It shouldn't be rude for rules to change too. I think the SIL was rude to include her friend from the beginning but it was what it was and should have been accommodated politely (as it was). But the OP wants to change that now.
OP, you definitely have the right to change it. Your MIL and SIL should be gracious and understanding about your decision. I would be if I were in their place, not happy maybe, but gracious. I think the only thing you owe them is to let them know as soon as possible about your decision. Though you don't need to, I think I would explain why in a kindly way. And personally, I would make it clear that this "no invitation to friend" is not a one-time thing, but permanent unless you want to confront this repeatedly. ("But why not this time?") Be gracious but be firm. And, yes, I agree that having your DH also tell them, perhaps separately, perhaps together, that this is the new decision is a good idea. Otherwise, they might, if they are so inclined, go behind your back, possibly resulting in a split (good son/brother, bad DIL/SIL). Let them see it is a family decision.