When does she start screaming?
What's her EASY?
Trust me, the mummy-instinct is there. It may not make itself known too often (mine doesn't

) but it is there.
I asked about the wind down, going to tell you to do away with it if you had one

Fret not about silly mis-informed comments. She is a tiny baby. I will say that DS does sleep on his own in broad daylight for naps, so darkness is not always required, even for spiriteds, but I think we'd have some issues if it was still light at 10pm and then only dark for 6hr...
Maybe I have been doing it all wrong and it is my fault that she doesn't sleep when we are out?
My mum and MIL had me feeling like a failure when DS was 4 months old too, constantly commenting on what I wasn't doing right... now they both acknowledge that I'm a good mum and I know DS well and meet his needs in a way that works for him and me & DH, all as a family.
Why wouldn't she sleep while she's been out running errands and visiting people? OVERSTIMULATION!!! and probably picking up on your insecurity and nervousness re: sleep too. We had the same issues with DS when he was a great sleeper at around 6 months and we visited IL's at their hotel and DS would. not. sleep. He was too hyped up and really OT and just wouldn't sleep - he was APOP-proof at that time too. They thought I was crackers for wanting to put him down for a sleep because he was 'so happy, just leave him, stop ruining his fun'

He was OT and OS and the raucous laughter and screaming were signs of that but they didn't get it.
From your descriptions, I'm not sure the rocking is really making her go to sleep, yk? What do you think?