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Hello I will assist today.
I am a U.K. solicitor working between the U.K. and the USA.
Unfortunately, as a US green card holder, you have no legal right to bring your mother to the USA. To be able to petition for her, you would need to be a US citizen and not a Green card permanent resident.
At best, ***** ***** apply for a B2 visa that would allow her to stay for up to 6 months each year. The other option is for you to apply for citizenship.
Afraid not, your wife cannot file for her mother in law, if you do apply for citizenship, once granted you can apply for immediate family green card.