Young adult science fiction I read in the 80's: boy goes underground trying to rescue father from plant

The latter parts of the answer are definitely a description of The Lotus Caves by John Christopher. The first part of is somewhat different, so you may be misremembering or confabulating two different stories. The Lotus Caves has previously come up here and here.

In The Lotus Caves, there are two boys, Marty and Steve, living on the moon, who go out exploring and eventually end up in a closed system of caverns that are filled with various parts of a gigantic intelligent plant. They want to escape, and they want to take Andrew Thurgood, an older man who has been living there for decades, with them. (It was finding Thurgood's diary earlier in the book that led the boys to the caverns.) However, Thurgood has no family connection to either of the boys.

The escape, as you describe it, is exactly out of Christopher's book though. They wait until the plant has pulled in the "flower" that it uses to collect solar energy, and the whole entity has gone dormant. They convince the Thurgood to help them find an closed-off exit, where they can break through to the outside. (Convincing him is not easy; after many years there, eating the plant's drugged food and subject to its hypnotic powers, Thurgood worships and plant and has no desire to leave.) Moreover, even after they all make it out, the plant wakes up and Thurgood goes back into the caves; whether this is entirely of his own volition or psychically summoned by the plant is ambiguous.