Keeping hateful, mentally unstable relative away a good idea?

My husband and I have come to terms that we must cut out his mother from our lives due to her inability to be kind, compionate, and above all, sane. She has always been very unstable but we dealt with it for a very, very long time only because she loves our 2 year old son very much. She often disregards our rank as his parents, however, and has made horrible comments about how she loves him more than us, etc, etc but we dealt with it. The last straw came 3 weeks ago, however, when she was angry at us simply for moving to a city further away from her home. She sent my husbands ex-wife (the mother of our son) an email spouting absolutly slanderous things that were completely untrue with no real reason except to attack us. We stopped communication immediately, including keeping her away from our son, and informed her that her email and blatant disregard for our feelings was to blame. All has been very well since, but my husband is now persistant that we should invite her to our son's 3rd birthday party in a few weeks if only to show that if she doesn't come, she will only have herself to blame (we have invited relatives that she hates and we are quite sure she will not come because of this). Regardless, I think it is unnecessary to invite her and that more of an example should be made not by her refusing to come herself, but by showing her that we meant business when we said that she has been cut-off from us entirely. Who is more correct in their decision to make an example? My husband, who thinks she should be invited just to show her that it is her own fault when and IF she doesnt come, or me, who wants it known that we are sticking to our guns and indeed cutting her off?