I enjoy working with you - it's nice to meet someone with eloquence and intelligence, along with qualities so very lost these days in the way of a gentleman. I also completely understand how you feel given the treatment you received over the years from someone clearly not on the same level and who diminished these relationships with ignorance and bias. It would have been so much more loving to at least be working together with both bio parents to co parent children growing up. How sad he dropped the ball and paved the road to this even being an issue.
So like it or not, here is my impartial observation and advice: Each individual has an unalienable right to exercise their free will. With that, your wife can call these children Prince and Princesses if she so chooses. You can call them Offspring One and Two, etc. if you will.
That being said, from what I glean of you from your writing, you're a bigger person than any of them and it occurs to me that you've lost sight of who you are by being muddled in who THEY are.
I would expect that you remain kind and generous and, well, 'classy'. Refer to these children as you would if they were anyone else's (besides this painfully low brow man's) - and we both know you'd say grandson, granddaughter, etc..
Otherwise, 'honorary' works and conveys dignity while noting they are not blood, but a choice.
Be who YOU are even when it's not easy. Be true to yourself no matter what others are doing or not doing. These are very easy words to say; very difficult to live.