I think there is some hyperventilating here. Business people have schedule changes all the time that require them to purchase a new ticket to a different location. Because cancellation penalties are so severe, the initial ticket is commonly worthless. Because of this, they don't even bother to cancel it. Since the destinations of the two tickets are different, there are clearly no shenanigans going on. UA will happily keep the revenue from your LAX ticket and not screw with your IAD ticket.

Go with your family to the check-in desk. State that circumstances have intervened and you will not be flying with them to LAX. More than likely, your family's bag allowance (especially if you are just checking one bag) will not be pulled, nor will their E+ seats be pulled. Group 1 boarding is more iffy, though.

If you show the check-in agent your ticket to ORD (and perhaps even obtain a boarding pass from him/her), and allow him/her to cancel your LAX ticket, they will probably be happy for your consideration to allow them to resell your seat on the LAX flight. I wouldn't worry.