need help to book trains or flights

I am going to stay 3 weeks in Japan and I need help to understand the best and convenient way to travel!
My husband, my 11 year old kid and I will have to go from TOkyo to Nagoya. Then from Nagoya to Hakodate and finally back from Hakodate to Tokyo. While in Nagoya we also want to go to Kyoto.
Unfortunately there are no more seats available at the discounted fare for foreign travelers with airdo airlaines to fly from Nagoya to Hakodate, which is a long trip and I am not sure what the cost and time of travel would be by train.

Any suggestion will bevery much appreciated! thank you!
Val