You're starting to even confuse me, reading this. Let's make things simpler. For the purpose of User accounts, the yahoo address is irrelevant. You should only use it in a browser to read your email or for My Yahoo content. It has No, Zero purpose for signing into a Win10 account. Get it out of your mind completely.
Now that, that is settled. Do both, either or neither of you have an msn or outlook or hotmail address ? Who do you want to be the primary account and admin, you or your wife ? The purpose of Family account is customize your own Microsoft account materials, such as Apps or Onedrive or to monitor a child account. Do not use it, and delete the account that you set up, it will only confuse you.
The primary User should have his/her own name and password/PIN, with or w/o a MS acct. The second user should have his/her Local Account, set up with his/her own preferred name and password which is specific ONLY to the laptop in question, NO other computer or phone. So, again, let's start with who has a Microsoft email acct and we'll go from there.
Follow this tutorial which is so brain dead simple that you'll be embarrassed -
Switch to Local Account in Windows 10
This is basically the 1st half of NavyLCDR's post. The 2nd half applies if either of you want to use a MS account to use the Store or Onedrive.
This is also how I set up family computers all over the country. I set up the computer with me and a MS account as the primary user and give the other computer user a Local Account with or w/o admin (you obviously want to make both of you admin's). The user with the computer in their house, happily signs in every day with their own name and their password and I only intervene with my account to remotely do updates or diagnose problems. This is the simplest way to set up two accounts, period. I hope you follow. Good Luck