The signal to your wifi box is good. And near it the wifi signal is strong so your internet conection is good. As you go further away the wifi signal drops(weakens) so you get lower access to internet.
Your son suggests a line adapter. This is a link using wires in the house to provide a good link to a second( or more) points. Here you can have another wifi box and get good internet access.
This is only normally a problem with very large buildings or ones with electrically thick walls. I assume the family pile is on a reasonable estate with the gamekeepers house reasonably remote.
Hi we all don't live in mansions similar to Dave's description of his pile, but even smaller houses can have internet comms problems.
If building extensions were done and or if aluminium foiled insulation .. is used in walls say kingspan type it will really scupper wifi signals.
Regrettably , the best way , and the cheapest way of ensuring reliable internet is by hardwiring cables .Well cheapest if you do the labour yourself. Depending on your house , very long cables properly terminated are available from maplin, B &Q and other major hardware stores. Your telecoms provider gave you a box which connects to the telephone line .... The modem. On the back of this there are typically 4 Ethernet outlets. A cable from any of these can be connected to a router giving another 4,8,16 connections. A cable from any of these going to either a computer , printer, settop box etc will provide internet . If you need it going to a mobile device e.g a tablet there are hotspot wi-fi nodes available.
That process can be extended almost indefinitely... Well up to 255 connections without bother.
Slightly less effective is to use a power line adapter. These are used in a minimum of two but can be extended up to four or more. The ethernet cable from the modem is connected to one of these and it is plugged into the wall. It then uses the electric mains wiring to send information to and from its mate. Provided both or more powerline adaptors are on the same electric circuit eg use the same electric phases, or are powered by the same switchboard, they can all communicate. You can reliably connect up to about 4 of these. Again some of these have cable outputs and some have WiFi nodes as well.
These are less effective for two reasons 1. The data throughout is lower than a dedicated cable , the response speed also drops as a function of the distance between the units , but does work over reasonable distances.
2. The protocols these things use require one to set itself as a master and the others as slaves. However sometimes they forget themselves and start squabbling.... So they are fine for a dual set but they can confuse themselves when multiples are used.
In case you are worried about your neighbours listening in on your powerline network... Don't be, the electric power meter at the mains inlet kills the signals