OK, let's take it one step at a time. When you change the administrator password protection you are not locked out of the site. Your browser (Safari) will simply ask you to enter the new username / password combination.
Let's start by completely removing that protection by deleting the .htaccess and .htpasswd files from the administrator directory.
Now let's see if Admin Tools is blocking either IP address (iPad and Mac). Follow the instructions in https://www.akeebabackup.com/documentation/troubleshooter/atwafissues.html Remember to do the middle process (after renaming main.php to main-disable.php and before renaming it back to main.php) from BOTH the Mac AND the iPad – basically, from each Internet connection currently blocked.
Afterwards you should be able to log into your site from both machines.
Then retry setting an administrator password protection. Important! One some older servers only the first 8 characters are taken into account. Try entering a password that's only 8 characters long to avoid any compatibility issues.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!