I'm not sure how devices decide to switch, but I know that they tend to want to hold a signal as long as possible before they switch to another AP. The reason is that if they switched to the strongest signal, if you are in a location where the signal is almost equally strong, there will be moments when one signal is stronger, then the other, within milliseconds, due to conditions. You definitely will not be happy if your phone is constantly switching between two access points (or three, in your case; I am sure that there is at least one location where all three have an equal signal most of the time), as the switch takes time and streaming, downloads, etc., would be constantly interrupted as the phone switches from one to AP to the other to the other to the other, etc., and battery life would suffer as well.
Unfortunately, there is little that you can do with most phones; they don't have many settings to change how aggressively and at what signal difference the phone should switch to the other access point/ extender / router, etc. I think the best thing you can do if you recognize that the signal is not what it could be is to toggle WiFi off and then on (or airplane mode on and then off) to let the phone re-connect to the strongest signal it finds.