Is this inappropriate to you ladies

So there's some history with this one girl my bfs friends with about six months ago he asked her if she wanted to take my place she said no bc she had a bf at the time now she has no bf and has started asking my bf to hang out and to come pick her up and ride around without me also when she sees him she flings her arms around him and hugs him closely and takes selfies with him it seems inappropriate given there past of kissing and him asking her what he did me and him have a two year old together and have been together for four years am i over reacting to think its inappropriate