One method would involve getting into their TNI box and setting up some kind of circuit that for example:
1. Emulates a dial tone when the phone is off the hook in the house.
2. Waits until at least 7 DTMF tones were detected on the house line, then dials the number you want called on the POTS line.
3. Then connect it into the house's terminals when it begins to ring.
If I recall correctly, it would be some kind of advanced gold box if you desperately want to do this, but I don't think there are any readily available schematics or easy solutions to accomplish this. This would also be very high risk, and most likely blatantly obvious that there is something sticking out/hanging out of somebodies TNI box.
Another method which would depend entirely certain services being offered in your area, and depending on your SE skills you might be able to have it set up as a business line with calling restrictions so that whenever the phone is taken off the hook it automatically dials a given number. This service is normally only provided for landlines that are intended to contact some sort of security/police department for emergencies only. The best way to find out about this possibility would to be just calling your phone number.
Another method would be to disconnect them from their telco entirely, and route all of their calls through your asterisk box with an ata (analog telephone adapter, i.e. sipura ), and then it would be very simple to just have asterisks configs just drop any dtmf data and call a single number. This method could be done if you there is any wifi + a powersource available to you that could power both a wireless bridge and the ata. This method could be pretty damn expensive, and obvious.
There could be other methods also, just be creative really.