Dear Vianna,
I feel your pain.
As I think about it, there are two delay times. One is the time between pressing the shutter button and the taking of the image; the other is the recycling time required until the camera is ready for the next pic.
The first can be the problem the camera has trying to focus because of poor lighting or movement (both may have been at play during your session). The second has to do with the time it takes the camera to write the image to the chip. The higher the resolution, the longer it takes.
I use a Nikon 5700, and of course I want the highest possible resolution for my resource images. If I am photographing a very active 2 year old, he'd be running into traffic by the time I watch my little digital hourglass do its thing. So for young kids I still go back to my film camera. I have auto focus on my regular camera, and it is still much better than manual focus.
As far as I know, the only way to get the delay under control is to go with a SLR digital camera, which is an economic jump from where you and I are. Then you can do rapid succession photos at high resolution. If you already have lenses for your film camera, it might make $$ sense to get its digital SLR equivalent. Mike M probably knows much more than I on this subject.
I am always dreaming of new technology (geek). When my ship comes in , it will probably have a Nikon D-70 or D-10 onboard. The downside though, is that the SLRs are quite a bit heavier than their non-SLR counterparts.
Not that this is particularly relevant, but I generally reccommend to my clients that children be about 18 months old at the minimum. I'm not sure that has anything to do with how squiggly they are since I just photographed some REALLY squiggly kids who were 4 and 5. Just be patient, flexible and persistent.
Good luck!