My DS is similar, although not quite as full on as your DD sounds. But if DH and I hugging, he will come over and push us apart or have to be involved, and if I am holding DS and DH comes over and touches me, he will slap his hand off. He does a similar thing if DH is holding him and I come over.

I think its just a learning "mine" thing and will eventually pass. I hope it doesn't cause too many problems with your new bubs!!