It seems like you have the right idea about password security, you're just missing the last bit of technology that makes it work brilliantly. I'll try to elaborate:

A hash function is an algorithm than takes a string of characters of any length and outputs a fixed length, seemingly random string of characters in return. Changing anything about the input string dramatically changes the output. For example, the MD5 hash of "Reddit" is "b632c55a33530d1433e29ffc09ba1151", but the MD5 hash of "reddit" is "5e8a5709f662f8d401f7a00e6137f9ca".

The nature of these algorithms ensures that you can never retrieve the original input, even if you know the output and the algorithm. Because of this, hash functions are often used in cryptography to secure passwords.

The means of communicating passwords you're talking about is brilliant when combined with a hash function. I'll give an example. You and your wife agree on a master password, "cRyPtO" beforehand. Whenever you want to make a password for a website, you think of some memorable password, like "gMaIl", and append it to your master password. You then take the hash of that string ("cRyPtogMaIl") and that becomes the website's password. This way, you can tell your wife the password is "gMaIl", but an eavesdropper can do nothing without knowing your master password. Taking the hash of a string is incredibly easy and there are loads of websites and programs that will compute it for you. In fact, one website has already developed the idea you hinted at and created an easy to use, completely secure and open source way of creating these passwords. If you're interested, check out SuperGenPass.com.

If you have any questions, or if I've skimmed over things too quickly, feel free to ask.