In this case, we would use either the indefinite article "a", since we don't know about your mom's vacation yet, or a possessive adjective (my, his, her, etc.). Once we know about the vacation though, you can use 'the'. For example, "Today, my mom came back from her vacation to Nha Trang. The vacation was very relaxing." Also, whenever we use "a lot of", the noun must be plural. Great work!