I will be travelling with 2 older teenagers. Can they wear the long shorts that cover their knees when in the Vatican?

To be on the safe side, I think that long trousers might be safest.
The thing is to look neat, modest and normal.

Slightly conflicting advice from tour companies.
"The dress code for entering St Peter's Basilica is specific. It forbids hats for lay men, shorts or skirts above the knee, sleeveless shirts, shirts exposing the navel, shirts exposing women's cleavage, shirts that carry profanity and excessive jewellery. Quiet, respectful behaviour is required, with no running, no shouting and certainly no blasphemy"
I wonder what they mean by excessive jewellery.

Another site says "There is a strictly-enforced dress code at the Vatican: knees and shoulders must be covered and men must wear full-length trousers".

On a trip this summer here's what I found.

Men, women, and children of all ages were admitted with shorts to the knees, or slightly above.

Women with shirts with just small straps were asked to cover up. Women with sleeveless shirts, with 2" wide strip of fabric on the shoulders were not asked to cover up.

Women with shorts which revealed more thigh than they covered were ogled by the crowd, then asked to cover up by the guards.

Many women carry light scarves that they can wrap around waist or shoulders if needed. It's always a good idea to carry one of those as they take up no room.

While there last year, I had on a pair of capris/gouchos (they came mid-calf) and a tank, but with a long sleeved cardigan over it. I had no issues. I didn't see too many people in shorts though, long or short.

This is October. When are you going? If it's before next summer won't your teens have long pants with them? They might get away with the long shorts but if the weather is cool, what is the point of wearing shorts and why take a chance on being turned away?