Perhaps if we put a comma after “appear” it will clarify the statement. There's a good book to read called Eats, Shoots & Leaves, which I would recommend to everyone who is concerned that there is absolutely no piece of punctuation in this sentence. So perhaps a bit of chosen punctuation will make the sentence very clear.
It was my understanding, from what Madame Demers said, that the committee would invite the concerned Canadian and Quebec civil society organizations to appear, following or as a result of the government's announcement to make maternal and child health a priority, at the G-8 in June that Canada will be hosting.