OK: update.
Met the woman today, have mixed feelings - I really liked her, and she did know a lot about dogs, and has a rescue dog of her own. 90% of what she said made sense, fit with what I've learnt here, and with how I feel. She gave some good tips, practical things, and lots of info on BARF diet if we want to try it (dh is keen - for the dog, that is, not for him 
).
OTOH, some of their stuff is clearly based on outdated pack theory, and the literature she left us irritates me - I have no intention of following any of that. Nor will I spray him with water (body, not face, but still) when he ignores my commands (not that she thinks I need to, but the literature talks about it 
.
Here's what I learned: to use a word other than 'no', which Mouse hears too often with kids around and takes no notice of. I'd already started saying a brisk 'Ah!' instead to stop anything out of order before it starts, iyswim - like chasing cats, jumping up, etc. Seems to work well - followed by lots of praise when he checks his behaviour.
I also learned that I'm not to give treats from my hand anymore for now, because since I have done Mouse comes and licks my hands/kids hands non-stop: hands=food. So now I'm to drop treats on the ground till the licking stops, at least.
I learned that I'm probably under feeding for the amount of exercise he's getting.
I learned that I'm doing lots of right things already 
I learned some things I can say to the kids to get THEM to do what I want around the dog (ie not follow/chase him around, not tell him off, not hang off his neck for 'cuddles'). They are already listening better to 'the trainer's advice' than they ever do to mine and this, I admit, is a major reason i wanted a professional involved
Have to say though, I've learnt more from Minimuu and others here!