Firstly, although you may want to clear your childrens names, I would urge you not to download any cheat files, even if you are just investigating!
Does the clan you play with stream to an anti cheat site? If not then maybe you should consider playing somewhere that does use anti cheat sites and then at least you can show them your and your sons records are clean. If they do stream to an anti cheat site and are still making assumptions, ask them why and what evidence they have to back up their claims.
Like Lluuu said, if they've made up their mind that your children are cheating then there's not really much you can do to prove otherwise. Even if you took battlerecordings, screenshots etc, their line may be just to say "well they had the cheats off for that time!"