Am I bound to obey my mother and family regarding their requests made late at night?

Obedience to parents is obligatory if they command something that does not involve disobedience to Allah, and they have a valid purpose, and their command does not cause harm or undue hardship to the son.

However, if obedience causes you unusual hardship, or leads to you missing prayers, then you are not obliged to obey them in such a case, while still being gentle in your apology.