All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The right of the mother in terms of being kind and dutiful to her is given priority over any right of other relatives including the father, let alone the in-laws.
In the case which you mentioned, you should absolutely give priority to your mother over your mother-in-law. Nonetheless, you should be wise in doing so, in a way that giving priority to your mother does not lead to negative effects on your relationship with your wife or with your in-laws.
For more benefit, please refer to Fataawa 87019 and 84942.
Allaah Knows best.