What would you do in my situation?

I had a fall out with one of my friends who is also a neighbour. I told my husband not to be too friendly with her anymore since she was crossing my boundries. She was my friend and never his, they only said causal hellos. He told me he won't stop saying hi cause that's rude . Not only that but after he dropped my kids off at school he offered her a ride, should I be offended or am I exaggerating? One of my kids told me she saw her get in the car with him. He denied picking her up. My 7 year old is very honest child. I'm furious