I dont know your boat, but some immediate toughts after reading your description:

Dont bring in the mainsheet to quickly on the new tack, get the boat going again before you sheet in. Sheeting out about 40cm should be enough.
Dont hurry over to the new side (unless you risk capsize), stay on the old windward hull.
Take care to steer trough the whole tack, dont let the rudders straighten out.

Good luck!