Unwanted guest (sorry it’s long)

So I work with this woman who is about 10 years older than me. She’s one of those types of people that has to be right about everything. Can’t even say the sky is blue without being told why I’m wrong kind of deal. She is rude and very disrespectful. For example, I remember when I bought my house she wanted to come see it, and first thing she did was grab my dog by the snout and say she had to let her know who the boss is. She is really unpleasant to be around and no one likes her at all. I’ve had several other people that are in the bridal party and some guests that will be invited ask me if I’m inviting her. My answer is no because I don’t want to be around her negativity on such a special day. Plus I’m terrified she’s going to criticize someone and start a big argument. And it could literally be anything, from not liking my niece’s names (they are twins and she doesn’t like that the names start with the same letter, she told me only an idiot would do that to a child) to a bridesmaids hair (also a coworker that is bullied by this girl). FH doesn’t want her there either.
So here’s the issue...she already invited herself! She told me at work that she already has a babysitter since her son is allergic to peanuts and she can’t risk his health. I pointed out that management doesn’t want me to invite a lot of coworkers because they can’t give everyone the night off (we work third shift). She responded with “Well it’s good I’m always up at that time anyway.” Then she sent me her address so I can mail her invite. I’m just flabbergasted that she did that! The problem is, if I don’t send her an invitation she will just crash it anyway like she has done my annual cookout in the past. I only invited a few co workers, and she showed up with her mom and just went right up to the food and started eating. Didn’t say a word to anyone the whole time. Everyone was so surprised when she showed up and did that. I feel like I can’t tell her no because I work with her very closely 3 days a week and I can’t handle the awkwardness. And if I don’t invite her she will show up anyway. So do I just have her come and hope she behaves? Or tell her in advance that I won’t tolerate her rude behavior? Or tell her I’m sorry but I don’t feel comfortable inviting her? I need a nice way to go about it because of the work situation...