Relationships are dynamic, and no two will be the same. You two have found a compromise which works well for you (or seems to). It’s good, but may not be possible for others.
You say you want more acceptance from your wife; Understandable, but consider this: How understanding would you be about another man entering a relationship with your wife, no matter how innocent? Bobbi is another woman, who is competing with your wife for your time and attention. Complete acceptance is a wonderful thing, when it happens – but it is the exception, which most of us will never realize.