360BLACKBEARD_TV from my understanding you are correct. You will lose all your multiplayer progress if you link a different EA account to your Steam account.
Also once you link a different EA account to your Steam account, there's a 6 month wait time before you'll be able to link a different EA account to your Steam account again.
It's also only possible to link one Steam account to an EA account. For example, your daughter's EA account is permanently linked to your Steam account and can never be linked to a different Steam account. Once you link an EA account to a Steam account it's a lifetime link and can never be changed to a different Steam account.
I believe all these rules were created to prevent game sharing. In the EA unlink article there's mention about merging two EA accounts, but I'd be worried about it causing game errors with EA login servers.
I've read players say they started having login error after simply changing their EA or Steam name. They can log into EA and Steam, but they started getting EA error codes when launching games. Something to do with digital rights management (DRM) authentication on EA's backend servers getting messed up.
https://help.ea.com/en/articles/ea-account/unlink-ea-account/
https://help.ea.com/en/articles/ea-account/ea-account-linking/