Well, I think sometimes screaming may be a part of it, until dad finds the magic trick.
My guy is only 9 months, so not quite a toddler, but also very strong willed.
Not very long ago, circumstances I won't go into here, led us to having dad put baby boy down. The first night or two was screaming. His dad laid down with him, gave him a bottle of expressed milk, held him, you name it, but the boy was ticked.
After two nights, my husband just ended up laying there and letting F crawl all over him, giggling, playing whatever. Not forcing the issue or having F lay down. F eventually just fall asleep sitting up! His dad laid him down and then left. This in about 15 minutes, no tears. And it has been this way every time his dad put him down since.
I'm not saying this is the solution for you, only that there probably is one. Dad just has to find that sweet zone where babe is sleepy, but not feeling like he is being compelled to sleep. They might also need to have their own routine separate from yours. For us, we bought an image projector and the show on the ceiling is a special treat for F, and he knows it is special to dad putting him down, so that helps.
And to be honest, it probably helps that his dad stays home with him two days a week and does all the bedtime routine...
Good luck! I can see how you would want to get this all ironed out before the new little one gets here!