The conflicts W and I had was that W would spend money on D (responsibly I might add) but because I was a big softy D would always want to get her own way and would act up with W. The only person who could control D was me. Daft as it may sound W didn't feel she was getting value for money with her little girl and felt she had lost her to me. Her words to me was that I had spoilt that girl for everyone else.
After W and I were physically separated for 2 months W struggled but managed to instil her form of discipline with D6 and when I returned I saw a different W and a different D6. In that respect the separation benefited all of us.
But I would say overall W and I haven't been too far apart in our parenting values.