I understand the problem you're having but let me enlighten you just a bit.
That time that your camera, what ever model, no matter who makes it, takes to shoot a shot is called
"lag" time. The camera needs that time to focus and expose so you get a photo. With out it you'd get nothing.
So, some cameras are faster it's true but the difference from camera to camera can be measured in
miliseconds and isn't even worth discussing.
Here's a tip and something I do often. You want a shot of your children doing what ever it is they're doing. You obviously know about the half press to focus and expose. As long as you hold that half press the camera is locked to that focal point and that aperture.
So, you're with your kids. Aim the camera and half press - then wait... be patient and wait for that right moment and fire. Do this again and again and sooner or later you'll have that shot or two that you really want. So you shoot a 100, they're only digital files. If you get only one or two you're successful.
I've been at this business for 30-years and I went on a major event not long ago 500 shots in one afternoon and evening. I kept probably 350 of them. Don't be discouraged because you don't get exactly what you want every time - that's an impossible goal anyway.
Buying a new camera may help your photo quality but it won't change much about the lag time.
