I think Happy mum = happy baby (as a general rule, obviously there are exceptions for most things), but I think that different things make each mum happy.
For example, controlled crying, or separate sleeping won't really make you happy because it goes against your parenting beliefs.

I think it comes from the general truth that when your needs are met, it is easier to meet other people's needs. I find this to be true in any relationship, if dh is helping me with things and meeting my needs, I'm much more happy to help him and meet his needs. So if a mum gets something she feels she needs (to have her need met), whether that be 10min of 'me time' a day, to a whole day off, or something else, then it helps her to feel a bit more refreshed, loved and ready to nurture other people.

Does that make sense?