[Manzanita]

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Is a raise on the turn the right play? And what do I do after a reraise from UTG?

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I would have raised the turn for the reason you give: charge your opponents to try to draw out on you. Besides those players holding a big diamond, there is a small chance that you are facing two pair or a small set.

Assuming that you raised the turn and UTG 3-bet, just call the raise. Since you have position, bet the river if UTG checks.

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what do I do against the check-raise as happened in the game

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The pot is big. You can't lay your hand down and your hand isn't strong enough to 3-bet. So just call UTG down. By the way, I strongly suspect that you are beat; a likely hand for UTG is something like AdTd.

-- Manzanita