Regarding the touching, your secondary just needs to tell your primary that she's straight. It follows automatically that she doesn't want a relationship with your primary. There's certainly nothing that says every poly relationship is bisexual. Whether she "loses you in the deal" is 100% up to you.
Regarding "alone time," I don't think it's your primary's responsibility to make sure you get alone time with your new girlfriend. That's up to you and your new girlfriend. Go on dates, go to her place, etc. If your primary is intentionally standing in the way or something, that's an issue that needs to be adressed.
I don't need labels to define me. They're sticky and I hate the glue they leave behind.