V.W.
You need to respect your son a bit. I had the same problem with my oldest when I got engaged - she had not seen or talked to her dad for over 7 years (his choice). It is hard for a child to let a man in - men do things very differently from us - your son is trying to adapt to this new type of authority - my advice to you - is don't let your fiancee get involved with your discipline - If you initate the discipline then you should finish it - don't let the fiancee jump in "mid-stream" it's too confusing for your son...
Your daughter isn't any better of a personality - she is younger and she is a girl - she is looking for that father figure in her life - your son is the "father" of the house - your son is also the "man" of the house. I know big shoes to fill - my children are without their dad - my 16yo and my 5yo son have taken on this role no matter how hard I try to let them be just children... they love mom and try to fill in and help.
I ended up breaking off my engagement - which I am very sad about - especially since I am pregnant, but my fiancee would not respect my parenting style an my children's needs for an adjustment. The bottom line is that your son needs to come FIRST - he is the child - your baby really - and the fiancee is the adult - so the adult needs to modify his behavior...
As for the ex - I wouldn't push the kids on him - the kids can feel how he feels about them - enjoy them and if things work out with the fiancee - the children will have a good dad - which is a blessing to you both - - -if not I assure you they will be okay...