There is NO special technique to deal with pianos that has an action that feels extremely heavy to you. You merely need to practice playing with heavy action pianos. There IS a difference in how you need to approach them but that comes with understanding your economy of action with your technique (this can be trained on both light and heavy action pianos, but it is easier to notice if you are going wrong with heavy pianos since they tire you out a lot quicker if you have inefficient technique).
The catch 22 is however, although it is easier to notice you are going wrong with heavy action pianos it is difficult to practice for long periods of time to solve the problem as you get physically taxed very fast, however with a light action piano, although you can practice for longer periods without becoming too tired you may in fact be able to get away with inefficient movements and the subtle difference between efficiency and inefficiency with regards to technique can become very close together.
Playing on very light pianos can be forgiving to your technique, i.e you may get away with inefficient movements without being punished with fatigue especially with rapid notes like long runs, arpeggios, trills, tremolos etc. I grew up playing with a Bechstein which had extremely heavy action and because I was a child and not fully developed I thought it was the reason why I did feel lactic acid burning in my hands/arms when I played sometimes. I still find that piano much heavier than almost all the other pianos I play and it still taxes my energy more so than any other piano, but I have learned to deal with it and save energy to deal with tiresome passages.
Points of relaxation and points of exertion in pieces are very important to notice and I can recall very strongly how it helped me deal with my old Bechstein as a youngster. For example when I studied Beethoven's Pathetique Sonata 1st Movement I would find the LH octave tremolos points of exertion because as a child with small hands it was certainly a challenge to try to maintain comfortably! Often I would feel lactic acid burning in my arm but as soon as I escaped those tremolos my LH was encouraged to try and rest while playing, this allowed me to gain some stamina in the hand/arm before having to deal with tiresome sections again. I found when you are playing passages which are less physically demanding you need to learn to relax as much as possible to try and recover some energy. I remember watching a science documentary on this using rats swimming in a bathtub. They would let them swim until they drowned which is terribly cruel, but the rats which they allowed to rest for 30 seconds or so then when they where forced to swim again could swim a lot longer than those who had no chance to rest. This means, points of rest replenishes more energy than points of exertion take from you.
In the end, just practice more on heavy action pianos, they are useful to learn from since your technique and economy of energy is forced to walk a thinner tightrope. You will come across many different pianos in your lifetime that are less heavy than your teachers but still more so than the one you play at home, but you will not feel too discouraged because you have had experience playing on your teachers one which is much more difficult. Growing up with a heavy action piano for the first 15 years of my playing certainly gave me the confidence to play on any piano, where I have noticed students of mine who grow up with feather light action digitals are horrified when they come across a heavier action piano so much so that it makes them think much less of their ability! It certainly can be a shock and demoralizing, but take it as a challenge and just realize one more point, that you should predominantly play the pianos that you feel comfortable with but puzzle over how to deal with others. It is good to have a strong preference in what action you prefer, this means when you ever go out to buy a piano you merely have to play them to know if it is the right one for you.
Why not go visit a piano store and play on the pianos. Find out the different action of each piano. Which one feels close to your piano at home, which ones might be lighter, a little more heavier and those that resemble your teachers and perhaps even some that are even heavier than that! It is curious to discover at all of these different type of action pianos, I find it interesting at least, each piano feels unique in some way (ignoring the sound it produces).
Certainly do not turn away from your teachers piano, things that feel difficult in life often teach us a great deal more than if we remained in our comfort zones. So please don't feel discouraged and press on!
Topic: Is my teacher's piano the bane of my piano existence?