The funnel clouds could represent the death of you mom since your sister replaced her in the car. The bad weather could represent the hard, bad times after your mother's death. When the weather cleared up, it could represent things getting better, and hard times passing and you were still afraid of tornadoes because you are subconsciously afraid of more hard times. Overall I think it is a dream reflecting your inner fears, and your past. Often in dreams others represent parts of ourselves.
Mothers are usually a very central family figure and represent a base or center.
Whenyour mother died she left that position empty. Your father is off dealing with her death by getting on with his life. You and your sibings are shifting back and forth trying to fill your absent parents postions in the family. Tornados are formed by two opposing energies, You are feeling a great deal of inner turmoil about which way to turn and perhaps trying to come to some type of resolution in regards to your mother's passing and the changes in your family. Birds are often spirits, perhaps your mother represents this bird.