More free parenting advice coming up!
I agree that the lying should be punished. Your judgement is right on target here. One interesting (to me) approach I've used for a first time (this sounds like a first time situation, maybe not first lie, but first time you've all had this combination of factors) problems is to ask the child what they think is the appropriate punishment for their misdeed. The answers have ranged across the scale. Too light, which I read as playing me or truly innocent mistake, too heavy, which I read as overreaction, or my previous heavyhandedness, or a very guilty conscience over another subject. This is usually worthy of another investigation. Usually the answer is an appropriate response, and as a bonus, the child understands the reason, the connection between their actions and their consequences.
As to the "gotta stay home" issue--this sounds easy to measure. Have each kid understand that they individually are responsible for talking to you on the phone at any time during your absence. They should be ready to show their presence, and adherence to the house rule by speaking to you when you call. Can't talk? That's
that child's problem. That takes the incentive away from the older to pressure the younger to cover for him. He's got to do his own talking.
As to being ganged up on...Oh yeah. Get used to it. Par for the course. Your best defense is to enlist the help of some mercenary surrogate parents--such as the crowd here in the cellar.
Good luck.