Interesting thread!
"Happy Mum = Happy baby" to me means that both people here have needs and both peoples' needs should be met. It doesn't mean mum puts her wants in front of baby's needs, though.
I know one Mum who is a happy Mum. Her baby "put herself to sleep" from 6w old (CCing), is "happy with strangers" (has no choice as Mum wants a social life) and "plays happily on her own while I bake/paint/scrapbook". That baby isn't happy the Mum goes out on a date with Dad every week, leaving Baby with a stranger. Mum is, but it's Mum's wants over Baby's needs here.
I know a time when I was an unhappy Mum. I needed help and support: I had bad whiplash from a car accident, DS was injured too and wanted to be held all the time, even with a sling it was agony. He could have been held by ANYONE - but MiL wouldn't come round and cuddle DS for me. (Found out recently I wasn't allowed to ask her because DH had and she'd said no!) Ignoring my needs was not helpful. Friends helped, but also had children so couldn't be around as much as, say, a retired grandmother could.
I'm happy when I go out for (decaff) coffee. DS is happy now to see friends and play. Win-win. But there was a time when he wasn't happy to be away from me. I kept him with me; he needed me and I wanted a half-hour to chat without him. Needs trump wants. Sure, it would have been nice to have a whole conversation but that wasn't happening, no big deal.
Whose needs first? Depends on the greatest need.
I've left DS crying in his cot for an extra 30 seconds before I'm by his side: if I hadn't then I'd have wet myself putting him back to sleep! Loo break trumps a half-hour of putting DS back down. Mostly DS's needs come before mine, but not always. I need to cook a dinner and DS wants to play: dinner wins. DS needs to get dressed and I need my BB time... DS wins (usually LOL).
DS was the one to stop co-sleeping, to stop breast-feeding, to start all his "big boy" behaviour (toilet training, sitting to table etc). His needs are being met as are my wants: I wanted him to tell me when to do this, I didn't want to have to push the issue! I missed him when he stopped co-sleeping but his need to be alone outweighted my need to have a body to cuddle!

