As long as you book 60 days out, you should be fine. If you are having trouble getting one for your whole party, try splitting your group and then playing with the times to overlap.
My other tip, which I learned way too late into our trip, use rider switch to your advantage. When you use rider switch, only half of your group needs a FP as the other half will be given a ticket and not have to scan their band to go through the FP line when you switch. Since you have little kids, you can maximize your number of FPs by using rider switch. So, if you want BTMRR and Splash Mountain, just split it half and half and then you still have 2 attractions left to pick for everyone. Make sense? Good luck!