If you installed the broadcom-wl driver from rpmfusion then a kernel update should also automatically update the driver. Where did you obtain the broadcom-wl driver?
As far as keeping the version and software up to date, the updates are recommended for security if the machine has access to the internet. It is quite possible to halt updates if you choose but you must decide between security and updates or no updates when allowing your daughter to access the internet.
The post by Flo below gives the details and the broadcom issue is related to the akmod-wl package which creates the kmod-wl package. Similarly to the issue with rebuilding the kmod-nvidia-* packages that can be directly related to rebuilding the kmod-wl-* packages. The same 3 steps apply with the package name changed.
Personally I have only seen this issue appear in 2 situations.
- A quick reboot after a routine update (including the automatic offline updates)
(I stopped automatic updates for this reason, and I wait several minutes after doing a manual update before rebooting) - the first reboot after a system version upgrade.
With manually controlled updates and delaying the next reboot the problem does not appear for me.