Can you break up your own full set when playing a Forced Deal?
The card text, as you quote, does indeed unambiguously prohibit trading away a card from your own full set, yes.

You might conjecture that this was not intended, but as it stands (with no errata or contrary ruling from an official source), card text prohibits the trade.

That said, Monopoly Deal is a lighter game, so I would certainly go with what feels right (obvious designer intent) over a strict adherence to card text. Just make sure that everyone at the table knows what the rule is and is happy with the change.