whereas I agree with kathyp, most people do rush it, I notice you posted this june 26th and then said it was 36 hours prior you put the queen in, and then gave the update about removing her today. thats 11 days with the queen in the cage. thats pretty long, imo. the bees will feed her and go mouth to mouth, and you should be able to tell if they are actually hostile towards her. as you've already done, by brushing them with your finger/seeing if they are biting the screen/etc. when you put the cage in, how did you have it facing, btw? I'm for having the opening NOT facing the wax foundations to either side, but up and down myself (o a queen box that is open on two sides with screening.
How you should do it I think really depends on what your plans are for the queen you have. if you really have none then put some candy in it and let them release her. one of a few things will happen, the two queens will fight, one will win and life goes on. the bees will kick her out or harass her out, life goes on, and that isn't likely. or she's the only queen and will be/is accepted...and life goes on. If you have a alternative for the queen then well, you probably do want to save her, but then it is on you to find at the least queens sign, or the queen. if you supplement with frames of brood/bees from another hive then next time do it with a frame of brood, bees and eggs that are two days old, and notch the bottom of the 2 day eggs downward at a 45ish degree angle. like in this video at the 30 minute mark, give or take:http://youtu.be/inGtBz0LB2I
they will make queens....and if you have a queen already, she'll kill them through the cells probably before they hatch...if not they'll fight and well one will win...life goes on, and keep supplementing with brood frames when you do it, and in 10 days after if you have them to spare.