Is it permissible for couple to help each other remove the hair from their private parts?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Bahz Ibn Hakeem narrated from his father, from his grandfather that he said: “I said: O Messenger of Allah! Our private parts? What is allowed for us to show and what should we conceal (from the people's eyes)?” He (the Prophet ) said: “Protect (guard) your private parts except from your wife and from that your right hand possesses; i.e., slave-girls.” [Ahmad, Abu Daawood and At-Tirmithi]

Therefore, it is lawful for both spouses to get pleasure and satisfaction from each other's genital organs by watching, touching and sexual intercourse.

So, there is no legitimate prohibition regarding removing the hair from the private parts of one's spouse, since more than that is allowed (as aforementioned).

Allah knows best.