Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
A husband is bound to fulfill the condition he had accepted at the time of marriage contract, i.e. to complete the study. Allah Says (interpretation of meaning): {O you who believe! Fulfill (your) obligations….}[5:1].
The Prophet (Sallallahu Alaihi wa Sallam) said: "The most worthy conditions to be fulfilled by you Muslims) are the ones by which you made the your wives vagina lawful for you."
It is very possible to seek a suitable solution for this dilemma. The husband can combine permitting his wife to complete her studies and providing their daughter good care. If the daughter does not suffer any harm in the college daycare then he should permit his wife to complete her studies. It is strongly believed that a child in this very young stage probably does not face any harm in such a baby care center. However, if the husband is not satisfied with the child care of the college then he should seek a suitable one and then should allow his wife to complete her studies. Know that Allah is aware of all the secrets of His slaves and He knows who wants to do mischief and who wants to do good. Both the husband and wife should have trust in Allah and should help each other in doing well.
We ask Allah to grant goodness for you and us in this world (Duniya) and the Hereafter (al-Akhirah).
Allah knows best.