Probably the first one it scans for and sees.
Download an application called WiFi Analyzer from the playstore. See which of the several WiFi access points has the strongest signal (the highest peak). I'd forget all the rest and just sign into that one.
Depending on where in the house I am, different networks are stronger. One may be very strong in one room and unusable in another.
The phone automatically signs in to networks I've signed into in the past. I'm asking what happens if there's two such networks available at the same time and place. How does the phone decide which one to connect with?
Normally this issue does not arise because there's usually only one network I've previously signed into available at any one time and place.
No I'm talking about my own networks but saying networks is probably a mischaracterization.
I have manually signed into each of those points of access on each of our devices, so the passwords are all saved on the devices.
What I would like is for the devices to automatically seek out the strongest connection in each place as I move around the house,, switching between points of access as necessary.
How big is your house? Perhaps you need to re-position it for more optimal coverage of the house. I don't think the version of Android installed on our devices seeks out the "strongest" signal. But you might try something from the PlayStore like Best WiFi