YOU make the decision YOU want. H is going to do whatever...and, though it looks very suspicious and you may be picking up weird vibes, you don't know the whole truth.
So...decide what your boundaries are. What can you live with? If you cannot live with a continuing/new affair, then put it all out there on the table. Call him on it--the roses, calling you her name, etc. Find out, then protect yourself if, indeed, this is a deal breaker.
If it isn't, decide how long you're willing to deal with it and what you're willing to put up with. My aunt made my uncle (my blood relative) move out of the house when he had his A back in the day. She pursued that legally, used the LRT, and they worked things out eventually.
Anyway, don't let H make your decisions for you. If what he's doing isn't okay, find out the truth and act, whatever that looks like for you.
SD
Me: 40 H: 43 H had EA from 2/06-9/06 Bomb 5/06 Piecing since 9/2006 3/2008: Boundary setting 7/2009: Boundary crossing~dropped my own bomb. 8/2010: Marriage finally on track!