Well, they are determined little shits, aren't they?

I remember doing stuff like this when I was mad at my dad but it never lasted for very long.

The advancement to "father" is merely a ramped attempt to hit Dad harder as so far Dad isn't letting the act get to him in their eyes.

But why is Dad thinking of rewarding his little robots? A science exhibit sounds fun, my son, but Father is pretty busy this weekend. Oh and my daughter, as Father just said, Father is pretty busy this weekend, but I'm sure the new restaurant is wonderful. Anything else , my two children, you two would like to ask before Father  dismisses you? 

Meh, and another week in the robotic mode won't hurt them a bit. Fourteen days of acting is far better than just seven. Twenty-one would be terrific. 

Hang in there. 

Your SO isn't seriously considering taking them somewhere based on thks behavior, is he?

I'm all for taking them out individually to get them to talk, but you certainly don't reward passive-aggressive kids with things they want.

Your SO needs to have the enough is enough talk. Things change that they don't have control over, and this is life for the next 5-6 years. They won't get to live with Mom full time. They won't get him to break up with you. His job is to raise them into adults, and if they choose to be cold and distant, fine. But your SO will be happy for himself and his family, and if they want to be miserable and push their father away, that's on them.

Yes, he needs to make it CLEAR that THEIR actions are ruining their relationship, and that he is utterly disappointed in their behavior. That he had hoped to teach them better, but if this is what they learned and want to act on, then they suffer in their own misery. He'll be the sperm donor if that's what they want, and he'll never contact them again after 18 if they ask that of him. But the niceties end today.

They'll be pleased until they realize no Christmas presents, or only practical gifts. Until he hires a babysitter on his weeks to watch them while you two go do something fun. He just needs to keep reminding THEM that he is open to having a positive relationship with them, but he won't be bullied by them. If they can't warm up, then they don't get to be part of his life because he refuses to be unhappy to cater to them.

I'd respond to them in the very same way~ Yes son, yes daughter and definitely not reward foolishness. I don't usually like the tic for tac but this game can be fun.

"Thank you son and daughter for your suggestions of places of interests you both like.  However this Father will not be rewarding his offspring for their cold, robotic behaviour.  Therefore, we will not be visiting these public venues.  Father will not be doing anything for you offspring until said offspring stop acting like cold computer bots.

Thank you in advance for your cooperation."

SD 20 has done this to me in the past when she would tire of me "parenting" her, it would infuriate me, it felt like she was being completely dismissive, now that I have little to nothing to do with her it matters very little.

I would mimic the behavior right back.  And I would exaggerate it so they would look and feel foolish.  Listen, these are kids.  And kids don't have the reasoning powers of an adult.  They think they are "sticking it to dad."  Dad just needs to NOT TAKE IT PERSONALLY and show them how ridiculous they are:

"Thank you Father for your concern."
"Your Welcome Son.  It is a part of my responsibility as a Father."  Said with an uppercrust British accent. Followed by a giggle to let them know how ridiculous they are.

"Thank you for dinner Father."
"Your welcome Daughter.  A Father is required to feed his offspring." Said with an uppercrust British accent.Followed by a giggle to let them know how ridiculous they are.

"Thank you Father for picking me up from school."
"Thank you Daughter for thanking me for picking you up from school.  This has been a stupendous outing for me."  Said with an uppercrust British accent.Followed by a giggle to let them know how ridiculous they are.

And then try it in reverse:
"Thank you Daughter for eating your dinner."
"Thank you Son for sitting politely on your chair like a big boy."
"Thank you Son for not picking your nose at the table."
"Thank you Daughter for using your fork.  IT is ever so polite."

The more ridiculous the better.  It will make them so mad they will eventually yell or lose their cool and you can FINALLY address the real issues.  The polite communication is a shield and a weapon.  Take a way the shield and the weapon and you can finally start to communicate.