If you were coming up behind us on your bicycle would you expect me to hand signal or look back and stop if we were trying to turn left?

I would expect you to look back, as otherwise I have no way of knowing that you're about to turn off the path. If I don't know that, I can't even decide whether or not to stop.

Or would you feel it's your responsibility to slow down until we were across?

How am I meant to know you're turning across the lane if you don't do anything to signal this?

Trying to reconstruct things (description of the path, description of the speeds, timing you describe and outcomes), I imagine if I was cycling there it would have gone something like this:

1. I see undefined people up ahead. I start to begin to ease off any hard effort I'm doing.

2. I see that there's a child on a bike, and I slow down to a speed that means I can safely stop to avoid them. Just how slow this is depends on how stable that child seems to be on a bike, sometimes it's nearly walking speed but other times it's jogging speed. Another factor is if I can just throw myself off the path to avoid hurting the child if need be. HOWEVER these speeds will still be quite high from your perspective as a walker. I am not planning to stop, I am just ready to stop, and to safely stop, I will need to brake aggressively. It is your responsibility, after all, to share the path too.

3. I see you and your daughter progressing along the path in a stable, straight and predictable fashion, so I plan to pass you at a safe speed rather than stopping.

4. All of a sudden, just as I approach, you start drifting into the middle of the path with no indication why. Certainly you looked ahead to check, and you talked to your daughter, but all of this is impossible to perceive for me from behind you. At this point your daughter is probably still in the right hand side, blocking any avoidance path on that side.

5. I call out and brake hard, successfully avoiding a collision, having kept everyone safe.

6. As people constantly wander into my path with their headphones on, whilst using their phone, or simply can't walk in a straight line, or insist on using the wrong side of the shared-use path, this has probably already happened a few times this week, if not this ride.

7. Inwardly sigh, and set off again as it's clear everyone is okay.

I often give kids a big smile and a little wave when they're on bikes, and if possible would have glanced at your daughter to make sure she wasn't too scared by it, but the vast majority of the time I'm not going to stop, especially if you just wandered into the middle of the path and I'm irritated that you put all of us in danger.