Login problem for multiple users within the same household

I have a few separate WordPress installations within one domain on GoDaddy hosting. I have been using WordPress for many years. However, now I have two sites that myself and my wife and children are using. One is a simple WordPress installation for a private personal blog I have been using for many years. The second is a WordPress network site where my wife and children each have separate private blogs within the network.

Here is the odd problem we are having. We typically access these sites via our Android tablets. Only one person can be logged into one of these two separate WordPress installations at one time when we use our tablets. If another user tries to login, they will not be able to see the login screen or they sometimes get the login screen and then can’t get past the login screen. If I test using PCs, this problem does not exist. All users can login just fine.

This is highly annoying. Has anyone else experienced this issue and know what the resolution is?