What is the ruling on obeying a mother's request to marry a second wife due to the delay in her first wife conceiving after four years?

The obligation to obey one's parents is subject to three conditions:

1. That their command does not involve disobedience [to Allah]. 2. That they have a valid purpose in what they command. 3. That obeying their command does not cause harm to the child.

So, if there is no harm to you in the marriage your mother commands you to undertake, then you must obey her command. However, if there is harm in it, then you are not obliged to obey her, but you must still treat her with kindness and gentleness.