New camera for taking pictures of kids

[Musky hunter 82]

So my wife and I have been truly blessed with the opportunity to adopt the two little kids that we have been foster parents for, for close to a year now. The problem we have is that we have a very base model camera (a Cannon power shot?) we're not really happy with the camera because the processor is slow, and it takes forever to take another picture. I'd like something where I can take multiple shots really quick and have a good quality picture at the same time (not sure if that's possible with kids). Our budget is right around $500 any help would be greatly appreciated, and the camera would mostly be used for taking pictures of the kids, we'd also use it for hunting pictures and fishing pictures A good zoom would also be nice I think the one we have now has a 10x optical zoom so something with at least that would be nice.

Thank you

[IA4PATS]

Congratulations! We just got a call on Wednesday to adopt 3 young boys. God bless you for doing that.