Council of Elrond

Recently had an play in which Carambor took a 2nd MH phase which is triggered according to the card at the end of the 1st MH.

My hand was over 8 cards. Now my argument was: The 2nd MH was trigger in the 1st MH so I never reached the end for the final discard back to 8 My opponent says a new MH was created so the 1st must have been finished aka a discard to 8 must have happened.

Any guideance here, thanks

End of M/H phase (and any phase) is a period.
In the period, some actions are triggered (and declared automatically), some other actions may be declared by players (e.g. Caramor's ability).
When the period ends (i.e. all chains of effects in the period are finished), a completion of M/H happens. Hands of players are reconciled, site of origin's card is removed from table (if needed).

So your opponent is right.