First of all it's totally normal for teens to not want to go for weekend visits anymore with their parents. All they want is to be with their friends.
He's probaly not gonna ever have much of a relationship with your baby his half brother, they're to far apart in age and never see eachother. Plus it's not high on the agenda list for a teenage boy. Just some baby to him.
As far as the lying as much as it drives you insane and it would me too. Stay out of it. If your only seeing the kid 1-3x a year just blow it off and bite your tongue.
He's hardly a child anymore almost an adult. Encourage your husband and support him to have a relationship with his son but back off a bit. You can't force anything.
All this energy you have at being frustrated at him direct at your own children in a loving way and use all that energy to do something fun or special with them.
You could be the greatest step mom in the world and be completely fair and take your step son with open arms but you'll always be seen completely different as the wicked step mom. Be supportive, pretend to be happy and leave it at that. Don't get in the middle of it. Let your husband deal with it. He probaly knows his son is lying but it hurts to much to admidt.