Hive#2 was queenless for at least 2 weeks. When I inspected it, there were no eggs. I ordered a queen and by the time I got her installed most of the brood cells had uncapped honey in them. (NOW WHAT)
Replace a few frames of capped honey with new frames (with foundation or starter strips). Freeze the frames you've taken out, then when you add a second box, you can thaw these frames (for 24 hours) and then add them to the new box.
They will quickly clear a space for her to lay. Trust the bees.
When your queen arrives you could always take a frame out of your #1 hive that has brood / room for brood, and swap it out with a frame of honey out of your # 2 queenless hive. If your #1 hive has more than one frame of brood & or room for brood that is. I agree with Micheal also though, the bees will make room for her to lay.