I fully understand your concerns about wanting a school that is a local school for your child. I also accept that the level of building work in Broughton is clearly going to increase the number of children in the area.
However you need to consider the bigger picture from Flintshire LA perspective. Some areas do have real problems with numbers (Hawarden, Sandycroft etc) but you have other schools such as Penyffordd and Higher Kinnerton, not that far away. So my first question would be, have you been offered a place at a nearby school?
If not then that does increase the pressure on places and on Flintshire to do something about it. There is no doubt that they could do something about it because they could put a mobile on site without any major problems to take a bulge class of 30 reception pupils, but that is not a permanent solution. £500K is only going to get you 3 more classrooms in all probability, which is unlikely to be sufficient over the next few years as the population continues to rise.
I would also ask the question whether the builders have actually handed over the funding yet, as quite often unless the LA are on the ball in terms of agreeing something before the builder starts digging, the funding is only paid when the development has finished.
I think I would concentrate on trying to push Flintshire Council to get a mobile on site as an interim measure, as that is the best you can hope for in the short term. I don't think that a petition will have any effect, what you need is to get to the right people in the Council with an appropriate amount of local publicity.