First thing to do is make sure there isn't WIFI issues. Stay on the land line for a while until you are satisfied there isn't any. If the problems persist, then...
- Make sure the DHCP setting in your router is disabled. It may be fighting with your parents router and creating IP conflicts.
- Get access to your parents router and check for the Maximum Number of Users setting in the DHCP Server Section. Try increasing the number by a few.
Are you or your parents trying to use a static IP? Conflicts can arise when a DHCP server tries to assign an address in use by another device. If the device must have a static IP, then make sure it's outside of the DHCP server's range.
There's many things that can be an issue. Hope these help!