This is what I find for Queen Trishala's dreams:
The first dream Queen Trishala saw was of an elephant. She saw a big, tall, and impetuous elephant. It had two pairs of tusks. The color of the elephant was white and its whiteness was superior to the color of marble. It was an auspicious elephant, and was endowed with all the desirable marks of excellence.
This dream indicates that her son will guide the spiritual chariot, and save human beings from misery, greed, and attraction of life.
I do not think there is any particular significance of these dreams other than all good and auspicious things seen by Trishala. The elephant with one tusk would not have been auspicious (broken), so two tusks.