How can I deport a green card holder?

Asking this question for my mom. Story short, mom is a US citizen, got married at the Philippines 6yrs ago, petitioned his husband and arrived here in US 3yrs ago, the 1st yr or married was good, but then as it goes on and when he received his green card, he started acting on his own. Doing his own thing without notifying my mom and been planning things behind her back, competely just treating her like she's no one. He went back to the Philippines last yr and lied about it to my mom. After 6 yrs or marriage my mom found out that he has another son there, and keeps contact with the other women, behind my moms back. He verbaly abuse her for asking questions, she didn't get the answer she needs. Being such a loving and nice person (my mom) he took advantage of it and keep doing it. Just 4 months ago, he quits his job here and left to Alaska without talking to my mom about it. He did it all behind her back and me, (I signed the affidavit of support for this guy by the way). Not knowing when he's coming back we heard rumors from friends that he might be going back to PI. With paper works to bring his 2 daughters and the other kid from another women. my mom would like to stop that.