It sounds like the badge is for the Royal Armored corps. If the mailed fist is vertical with a circular surround topped by small arrowheads and the whole thing is topped by a crown then that is the badge.
The other badge you describe sounds like one of the hourglass symbols used by various Army Tank Brigades. But, the color combination is not familiar to me so I cannot say which brigade it might be.
That's the best I can do from the description you give alone.

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