Does Halachah obligate one to vaccinate ones children? We feel very strongly against it and our Rav here in Canada said there is no need but in the US we would be obligated. How about Israel? Is it required by secular law? Can it be avoided? What is the principle behind it?

Generally there's an obligation to save ones life when in acute risk even if he doesn’t want it to be saved. If there's no acute risk a person can refuse treatment as long as he has a good reason, believing that the proposed treatment by the doctor is bad or useless, may qualify a "good" reason. (Mor Uktzia 328, Igrut Moshe CM2 73) If refraining from vaccination is a risk of life according to the doctors, one must take them. If the above statement is not agreed by all medical practitioners one can decide not to vaccinate as long as he is in no danger. In terms of the laws in Israel you should consult a legal authority.