EDIT : But it's not as simple as I thought with extra attacks.
Yes, current multi-attack implementation seems a bit confused. It seems from my testing that multi attack triggers on attacks with main weapons only (including basic attack and weapon skills) - as a second attack you can use other martial skills, like throw, however starting with throw won’t grant you an extra attack. I imagine something like that would happen with full-action push.
Yes I've noticed that too with throwing weapons.
I've finally found how to be able to shove then attack... It took a long time to me but really, it takes 3 seconds when you know where to look at. BUT if I attack first I still can't use shove as an extra attack^^ Confused, as you said... But I guess it is extremely easy to do for players a bit more used to this than myself.