Yes. if you lay down while reading, the improper position and overtime will cause damage to the spine and neck. So you will find uncomfortable to read. So you are easy to get eye strain if you read while laying down, which can cause damage to your eyes easily.
Yes, your mother is right. When you read laying down, you can hardly control the distance between your eyes and books. Also your eyes are not in the same line, either upward or outward. It can cause crossed eyes easily. So you should listen to your mother's suggestion.
When you lay down, your eyes will bear much pressure and cause tired eyes easily. You will also develop myopia in the long time. My sister now has to wear glasses because she often reads books laying down on the bed!