There really is no need to remove her at all. you can wait until she lays new eggs, notch say 2 places on each side of 2 frames, stick it into a builder box, with workers honey and pollen frames on the outside and a few frames of nurse bees and they will make queen cells for you. And you just let the original queen and original hive continue on its merry way.
Do a search for OTS queen rearing. or On The Spot Queen rearing. you can then if you so choose, remove the queen cells from the builder hive, insert them one by one into frames and make a separate split for each one, or use each frame separately and let them figure out who survives for each colony, making splits, and then do it all over and over again. of course you are depleting your initial hive of offspring, but then you also potentially have many queens laying at a time which is far more efficient, and you can then do combines later on back into the original hive before the late flow, if you have one. 2-3hives of 30,000 bees has been shown in some studies to not produce as much as one hive of 60-90,000 bees, plus a larger hives over winters better...but then of course you have one queen too usually. (you can actually have more but not getting into that.) and 3+ hives tend to combine actually better then doing a 2 hive combination actually.