Unfortunately, There is no way to get the same green card back. He would have to apply again by someone petitioning for him. Since your parents are permanent residents, they can submit a petition for your brother. However, since he is from Mexico and I am assuming that he is over 21 years old, there is a very long wait time for a visa to be available for him . Right now the wait time is 20 years for Mexico. This time can change and be faster or slower. If they want to do it, they would submit an I-130 petition http://www.uscis.gov/i-130.
If 10 years have passed when the parents' petition is ready ,then he does not need a waiver. If it has been less than 10 years since 2013, then he will need to apply for a I-601 waiver and I-212 application in order to be allowed to return to the US.
When his daughter turns 21, she can also petition for him and there would be no wait time because he is the parent of a US citizen but she has t be at least 21 to do it.
In the mean time, he can try to apply for a tourist visa or get a job in the US and apply for a work visa, or come to study and get a student visa. If he wants to do this, he would still need a waiver that he applies for at the same time as the visa. It's called the 212(d)(3) visa and it is only for temporary visas. Here is more information about it http://www.nolo.com/legal-encyclopedia/applying-nonimmigrant-visa-hranka-waiver.html
Good luck to you during this process and I hope this answer has helped you!
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