Each teacher will have his/her own style and interpretation of the book technique. You will also develop your own style which suits you. It should be "correct" but not a carbon copy of any particular teacher.
You don't say how long you have been dancing but as the hand to hand is a beginner figure I shall assume not too long. You will find that even one teacher will tell you different things on different days depending on which aspect of your dancing he/she may be concentrating on. Straightening or bending of the knees will appear trivial when you start playing around with the timing and speed of turns etc.
My personal preference is for the legs to be straight (not stiff) except when moving into position. In particular when stepping back in hand to hand, the front heel will lift but the leg should remain straight. Some people bend this leg quite sharply which I think makes them look as though they are riding a bicycle. Just my opinion.

Finally, since your current teacher will be working with you to develop your dancing, I would go along with him and not worry about what your old teacher may have said last year. If you really feel he's wrong you could tactfully mention you were taught differently and let him argue his case. It will show that you are thinking about your dancing and it's sometimes useful for a teacher to re-evaluate what they are saying.