Answer
(Fatwa: 1329/L=389/tl=1431)
(1) Your wife is right in saying that it is not necessary on wife to serve husband’s mother. However, it is the moral duty of your wife to consider your mother like her own and consider her service a blessing. You can convince your wife with politeness and wisdom.
(2) It is not necessary to be present near mother all the time. If you stay away due to need it is acceptable. However if your wife does not serve your mother, it is better for you to keep some mahram girl near your mother who can serve her. It is not right to divorce your wife if she is not ready to serve your mother.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband