Originally Posted by Mike Jacoubowsky

As noted by others, UA doesn't allow you to drop out any part of your itinerary without cancelling the rest (with the exception of irregular ops or schedule changes). Of course, if it was your last segment, no biggie, they're unlikely to come after you and they cannot retroactively cancel flights you've already flown.

But, why would your situation involve two ticket changes at $150 each? Why not have one of you take care of the dog and the other fly on the plane? Then it's just a $150 fee, which is as much related to the joys of dog ownership as the joys of flying. And in my household, if we can get by with a $150 fee for anything having to do with our dog (or chicken or rabbit), we feel quite fortunate.