This is what I have there may be a newer model. It is an AP out of the box press some buttons and it is a repeater.
As far as range for WiFi, outside maybe 300 feet to a small tablet. The antenna in the remote device is the problem. The designers seem to have zero idea what an antenna should do. They think impedance matching is the goal and put the highest loss SMD resistor antenna in,
In using a second AP you need a Cat5 run from your router to somewhere outside near or seeing the other house, buy some POE widgets so you don't need to wire AC near the AP. You can use any old AP this way.
Try this. Assuming you current AP isn't toasted, unplug it from the network and move it to a point of your house near the other house, plug it in to AC . Go into the other house. How many bars? Is it getting a reliable signal? You wont have a network connection but you shoul have carrier.