The easiest solution as I see it, without buying expensive mesh systems, is to plug the powerline adapters directly into a wall socket (not a extension lead/adapter) to avoid interference to other devices etc. If router a which is connected to the phone line has a IP of 192.168.1.254, give the second router a easy to remember IP address (say 192.168.1.200). Leave DHCP on for router connected to the phone line, but turn DHCP off on the second one. If the routers are dual band, unsync the 2.4 and 5G bands, and give each of them a unique SSID network name (no two SSIDs will now be the same, but the passwords can be). Save all the settings to both routers and now via the powerline adapters, connect them up via the LAN ports on each router. Yes you will have to manually connect when you move from point A to point B, but at least the connections will be stable. A device not recognising a correct password in my experience is down to wifi interference, possibly caused by a overlap of the two identically named access points. Hope this helps...

The problem is that roaming between the access points is not working. Not that a stable connection is not possible if you don't move. The problem with invalid passwords is most likely that there is confusion from the device about talking to the access point so the authentication is getting split brained between the two points.

Most people want to be able to wander around their home with a working WiFi connection and not have to think about switching your connection from one access point to another.

The problem is that WiFi was not originally designed with roaming in mind. Hence the much later standards 802.11k and to some extent 802.11r to make roaming actually work, and a whole load of proprietary hacks in the interim.

The solution is simple as I have explained, you need a 802.11k system. Either you are willing to pay for it and your WiFi just works in the way you might expect, or you are not willing and/or able to pay for it and your WiFi will have constant issues.

All I can say is that when I fixed up proper roaming WiFi for my brother and then my sister they where really please even though it cost quite a bit of money. More than the Black Friday deal on the BT Whole House system is at the moment. In both instances I tried the cheap hack that was tried here. In both instances the issues that the OP have reported occurred. My brother was the first to get fed up and splash the cash for proper system. The success of that was enough to convince my sister and her husband that spending the cash on a full on system was worth it.

For me I am lucky in that a carefully positioned ceiling mounted access point does the job for the whole house.