For your own health, and that of your children , you need to try and leave this issue alone as far as your ex is concerned. If you are in your kids lives and you know that ex's new partner is likely not to be around too long then I would focus on your relationship with your kids and let his fizzle out in its own time.
If I was you (I'm a mum with an ex who has tried to have other 'mum' s around) I'd ignore the the use of dad for him and always use his name instead but I wouldn't correct the children, they will get there themselves in the end, mine have :-)
It's hard but I explained to my children that you get one mum and one dad who are the people who made you/ were there from the start/love our always but that other people will come into their lives because mum and dad don't live together and it's OK to like these people and to have fun with them but mum and dad will always be mum and dad.
If there is a new baby then 'dad' will reasonably be a term in operation in the house again and it will take time for your kids to work out the new relationships but they will get there if you stay strong and support them in doing so.
I agree with the above just allow it to continue, i know it must hurt, and it's confusing for your children but i wouldn't get too worked up over it, as said concentrate on your relationship with them.
I would though explain to them that they may call him dad and in a way he is, but that he is their step dad and you are their natural dad and always will be, don't get into talking down about him or their mum, but explain the difference to them in a way they will understand.