I admit the three things she mentioned didn't seem like a big deal to me, especially the hugging. Sheesh, people hug all the time; it in no way implies some kind of a romantic connection.
The best compromise I can think of is to go easy on the touching *when she's watching.* When she's not around or steps away for a minute you have an opportunity to show some affection without offending her. But I don't know how tightly she clings to him. It sounds like she might have some control issues.
Keep in mind that your ex chooses to be with her, so he has to accept a share of the blame for this censorship that has come between you and him. Depending on how important it is to him to maintain physical touch with his exes, he may want to consider looking for a new partner. It's his decision.
Sure, find out if you ex is uncomfortable with the touching. At least then you'd know where you stand on a theoretical level.
Love means never having to say, "Put down that meat cleaver!"