Is home sewer pipe relining a good idea? As opposed to trenching and
laying in a new sewer pipe.

Does it really last 50 years like the plumbing companies that do this
claim?

The drain is supposed to have a leak and fill with water at a low
spot, and that's why the basement toilet will back up if the other two
toilets are flushed in quick succession, or if the washing machine
drains.