sparkly, that's totally unfair. First of all, I don't think (have I missed it?) that OP said anywhere that the ex is a 'single mum', she may well have a partner herself. Not that it is really relevant anyway, because by your argument, inconvenience and difficulty to the adults makes no difference whatsoever, right? 
And as far as the kids missing out on party bags etc...what about the events/activities that the kids might miss out on because they clash with plans made without the dad knowing? As OP said - what if OP and the dad had made their own plans to do something with the kids?
What's best for the kids is communication between the adults who care for them.
I agree with *ladydeedy8, if there can't be mutual decision-making by the two parents, then invites for things that are occuring during the father's time should be dealt with by the father. That means he has responsibility for replying to them, arranging transport, sorting out birthday gifts, whatever else is required. Of course, this would require the dad to be reasonable and considerate, too.
OP, would it be possible for your DP and the ex to set up a shared calendar online, just for the kids' social lives, appointments, etc? I'm thinking of the sort of thing I used to use with my boss, back when I was a PA...when she received an invite to a meeting, I'd put it on the calendar and she could accept or decline; we could then both see what was going on for her on a given day. I obviously don't mean that you'd have to share with each other every thing the kids were doing when they were with you, just when something came up that was on the other parent's time, IYSWIM. I realise that the ex might not go for this, if she is really very unreasonable or disorganized or just can't bear any level of communication with your DP at all...but it is less direct than phone calls or emails and maybe she'd see the benefit in it too? Sorry if I am being overly optimistic.