In the example the OP gives I am confused as to why she doesn't know they are having sex. She is right in the room. Do they have to ask permission if she is right there? If my lovers are initiating sex and I'm right there it would seem awkward for them to stop and ask.
She also puts it as permission/knowledge. Maybe her lovers are unclear how that works. If I were in their position then I would be confused. I think she definitely needs to clarify this part.
One of the ways we combat this type of jealousy issue is by always telling the third party in a playful way, especially when it's after the fact. For instance, we work hard to have dinner together each night. During discussion of our day we will slyly mention if we had sex. This way the third person finds out and is included, and the door is left open for sex later on that night, to include all of us.
Although my husband and I have been together 10 years and our partner joined us just recently, we try to see all relationships as equally important. For instance, when I miss out on sex they have as a couple, I think of it as missing out on sex with her as much as him.
I apologize if this is not entirely clear. I find language inadequate to describe the tangled web of life in a triad. I never meant to be dismissive of the OPs feelings. As the wife in a triad I empathize with her situation, but I do think that the best things is to just keep talking. Talk talk talk about all your feelings. When you hide things from your partners it builds walls and makes people take 'sides'. It helps to have it all out there so the three can think about it and come to an agreement. It also helps to remember that relationships constantly evolve and change, especially triad relationships.