Nothing that you have described about her sounds too odd to me. You, OTOH, sound kind of worked up. It can be very hard to coordinate the schedules of three people and you don't even know who the 3rd party is (or do you?). Yes, you would like a reply, even if it's a "Those days don't work for me and #3 together. Sorry."
People just plain get too busy to answer every contact and, sometimes, real life gets in the way, too.
Does your #1 lady tour regularly? That could be a factor. She is busy planning and touring.
Is she "high volume" or "low volume"? That's a real touchy topic and a subject of mythology but the answer doesn't even matter. If she is very busy, she's getting and answering lots of other calls. If she is low volume, she might have had a good offer that filled her monthly quota and is less needy to set this up this month and wants to push it off til next month.
When she says she can see you alone, it could be that she just wants more one-on-ones with the 3-way as bait but it could also be that she just can't get #3 to schedule on short notice.
Who is #3 and will #1 let you do the coordinating? Is #1 afraid of losing you to #3? (I doubt that's the case.)
What is a reasonable number of DAYS? I think it can take weeks or even months to set this up and that wouldn't be unusual. (I don't do a lot of 3-somes, but I travel and ladies I like to visit travel. Sometimes we miss each other in a given city by a day or two or more. I just wait for the next chance which could be months away.) I, personally, wouldn't waste my emotional energy on this and I'd ask #1 to contact me when she and #3 become available together, probably when the rent or car payment is due. Then, I only have to worry about adjusting my schedule, not theirs.
I wouldn't call her. I would use the "let me know when you're available" email. If you do call, don't sound desperate, crazy or accusatory. IF I were to call someone like this, it would probably be a brief, "I hadn't heard from you and just wanted to make sure you were okay. Send me an email when you have a chance so we can get together again."
I had to make a lot assumptions based on your story but I hope I'm not too far off base. Calm down, play it cool and move on to the next ad