Hey!
Tag team is a noun that means when two wrestlers take turns in the ring.
However, it is quite commonly used as a verb in North American slang, like in your example. In this case, the past tense ‘ed’ ending would be on team, as in “tag teamed”. It would be correct to say “I tag teamed with my wife” or “we tag teamed the drive to Spain”.
I should also mention that “tag team” can have a sexual meaning, so you have to be a bit careful with it!
Hope that helps.