He's not handling it well by bringing your son into the adult drama and it stinks that he wasn't there at first to help raise his son, BUT he is involved now & I kind of understand where the bio dad is coming from... my husband has dealt with the step-dad being called "daddy" since she was very young... it rips his heart every time. He's a down to earth, WONDERFUL father who's as involved as his ex lets him be. He's happy that the step-father is also involved and loves his little girl too, but it still hurts him to have to share that title. We've always discouraged my step-daughter calling me "mommy" - I'd say "that's not my name silly!" (because i've seen how much it hurts my husband to be on the other end). She calls me JoJo. His ex she flipped out when she thought my step-daughter was calling me mommy, so she saw how bad it can hurt.
My stepdaughter and I have an amazing relationship and a name doesn't make or break that. She knows i'm one of her parents and that i consider her a daughter, even though we don't use the "traditional" title.
My personal opinion - I think when the bio parents are in the picture, those names should be reserved for them... maybe come up with some other cute nickname for him to call your fiance?
Children adjust well to change if you don't make it into a big deal, and make it FUN! Its not stressful unless the adults make it stressful. I don't think you should make him chose between his father and stepfather's wishes, he might feel stuck in the middle which is way worse than having to switch how he refers to someone... you're the parent, you can decide these things at his age and teach him what to call people.
My husband never wanted to put my daughter in the center of the drama, so he mentioned it to his ex & then just sucked it up, but it stinks that his ex didn't give a hoot that it hurt him so badly. My husbands feelings have nothing to do with insecurity in his "dadhood". I can't imagine many parents would like to see their children calling another woman "mommy" or another man "daddy". Would you?
When my step-daughter got older we reinforced it was ok to call him what she wanted, but asked her that at our house to please call hiim "stepdad" and not "daddy"... we never made a huge deal about it, just made it a matter of fact statement and she never flinched. We just told her it was too confusing since we never knew what "daddy" she was talking about. We even joked when she "slipped up" and always kept it light, now she just automatically calls him stepdad at our home. Its made it easier for my husband not having to hear it, even though he know she still calls him that at her mom's.
Plus, not that it makes it right for your ex to put your son in the middle of this, but is he going to continue confusing your son by telling him he's wrong to do what you say is ok? wouldn't it be better for your son for you to be the bigger person so that your son doesn't have to get involved with the adult drama?
Good luck, i know things are easier said than done... especially when we're not the ones dealing with the situation. Hope you can find a solution that's right for your son.