I have a lot of trouble with that philosophy too, because we as Christians don't take a hands-off approach like that in everything. We don't sit in the driver's seat of a car with our foot on the gas and wait for God to direct the vehicle where He will. We may pray for direction on where to go each day, but we facilitate the actual movement of the vehicle to get there. And if it starts veering to the right, we don't just decide to travel right; we correct it. I think the decision of how many children to have and when should be planned in prayer, but achieving pregnancy or non-pregnancy requires actively timing relations and ovulation (any number of ways). It's a biological reality, not a mystery. Just because we choose to exercise our biological abilities does not mean it is always right or wise. I think it does mean that God will bless us where we are, but that does not necessarily mean He put us there.
I've heard sermons differentiating between His "perfect will" and "permissive will." He may permit you to have children and bless the decision, even if that was not the ideal situation. But just because it happened doesn't mean it was is perfect will for it to happen. Maybe it just means He gave you the tools and you used them, and it worked... like with any other venture. Simply rolling the dice by ignoring all the biological factors that are necessary for conception, even when you know they exist, is not in my opinion following God's will. It's playing Roulette.
I also think that if birth control was inherently wrong, then the Bible would have at least some indication of that. It's pretty clear that Onan was disobeying a direct commandment given to him, so it's kind of hard to extrapolate Genesis 38:9 to mean that all birth control is wrong. So where is this hands-off philosophy coming from biblically?