How do you cook more successfully in a different kitchen?
Planning, planning, planning.  As you say, you are used to your kitchen and know where everything is.  Go over the recipe(s) in advance and locate everything you will use.  When you cook at home, you know where the measuring spoons are.  Find them.  Make sure there is one of the size you need.  You know you have all the spices, but put your finger on each one you need and open the jar to make sure there is enough.  You might even poll the other cooks to make sure you aren't all using turmeric and there isn't enough to go around.  Even better, premeasure the spices and hide them somewhere.  Decide what pan, cooking implements, serving dish, and serving implements you will use and make sure nobody else wants them.  When the gathering is large the house often doesn't have enough big ones.  Foil covered cookie sheets can be a lifesaver.  I find there are always enough burners on the stove to go around, but the oven can be a problem. If you do this the day before there is time to recover from problems.
Having done so, recognize that you are your own worst critic and are not looking for your Michelin star today.  There will be glitches.  Probably you can recover from them, perhaps with some loss of quality.  If it is small, nobody else will notice.  If it is large, they will share your pain.  It may become one of the family stories.  It isn't the end of the world.  I recently burned up an entire rack of ribs on an unfamiliar grill.  Fortunately there was some meat in the freezer for a replacement.
One challenge is the conflict in attention.  When you are cooking at home you get to think about what can be done before guests arrive and how you will share your energy between cooking and talking to guests once they arrive.  When you cook for a family gathering the guests are there already and competing for your attention long before the meal.  There are a range of ways to deal with this, but recognizing it in advance can make it easier.