Alfonos,
Welcome to catamaran sailing! As you might imagine, there are a ton of tips available for handling your boat in high winds. I can't recommend enough, Rick's book on "Cat Sailing for the 90's" or any of the Rick White videos - there is a ton of information in there (and you should be able to order them from this website).
A couple of key things to consider when tacking in heavy air (or anytime really):
1) prior to tacking, your mainsail and jib should be close hauled (in very tight) - you will be lucky to get the boat turned through the eye of the wind if they are loose - especially on a H16. It doesn't matter if it's heavy wind or light wind, they need to be sheeted tightly and the boat moving forward well prior to starting that tack.
2) Turn the rudders gently until they are fully (or nearly) turned. If you jam them over quickly, they act like a brake and slow the boat down. If you turn them slowly, it gives the boat more time to begin turning and it will carry more momentum through the turn.
3) Make sure your crew doesn't release the jib to early in the turn. The jib should be uncleated when the wind has just started to push in the leading edge of it. If you release the jib before you get head to wind, you are loosing power. You need the jib to continue pulling as long as possible.
4) Try moving you and your crew farther back on the boat to get the bows floating higher or out of the water when turning. The bows are moving sideways and pushing a lot of water when they are turning. If you can raise them higher there will be less resistance to turning. However, in high winds, you may want to be cautious about moving your weight too far back because the boat might flip backwards if the wind gets under the trampoline.
Maugan listed a good tip too - if you continue to have trouble tacking or are in rough water or are in a tight maneuvering area where you MUST make a tack, backwinding the jib will help you make sure you'll get through the eye of the wind. Instead of releasing the jib when you get head to wind, leave it cleated on the wrong side until the boat is safely on the new course - then change it over.
You also mentioned landing the boat onshore with a strong onshore breeze. I haven't tried this yet so I can't say for sure if this really works but practice 'backing up' in an open large place on the lake. Raise your rudders, release the mainsail, and have both you and your crew get out as far forward on the boat as possible while one of you holds the jib out to the side. I understand this will make the boat sail backwards pretty well. Once you've nearly reached shore, release the jib and step off into the water to stabilize the boat.