So, let me suggest some things:
1. The ONLY possible reason for the "strange" comb is improper spacing of the frames. When using foundation, you should run 10 frames. Only in the 2nd year should you reduce to 9 frames. When running 10, the frames are pretty much self spacing. With 9 frames, you must be VERY VERY diligent about spacing. Some beekeepers always run 10. The problem is that by the 2nd year, it becomes very difficult to remove the frames. Burr comb on top of the frames is also caused by improper spacing but is almost impossible to control. A box that is 1/16 to tall and a frame that sits 1/16 too high will result in burr comb.
2. A failing queen is characterized by an inconsistent brood pattern OR an excess of drone brood. In other words, a healthy queen will fill the frame with few open cells. A failing queen will have many open cells in a checkerboard pattern. An excess of drone brood means she is running out of semen. (However, in the midst of a honey flow, a healthy queen may lay a spotty pattern because she has a hard time finding open cells with all the nectar coming in.)
3. The most likely cause of the difference between your hives is "drift" in the original installation. Because the number of bees grows in an exponential increase, a small difference in the number of bees will make a huge difference later. If 10% of the bees drifted from the weak hive to the stronger in the first few days after installation, the starting point would be 90% and 110%. Do the math and within 8 weeks or so, the stronger hive will have twice the bees. In the first few days after installation, the bees are confused about where their home is. Wind and other factors can cause drift.
4. To boost the strength of a hive, pull a frame of sealed brood from a strong hive, bang it on its end in front of the entrance in order to knock off the bees, and place the frame of brood in the middle of the brood cluster of the weak hive. With packages, you should wait until you are sure the queen is released and accepted before doing this. If you have existing hives (from last year) pull from them to boost the packages as soon as possible. If you only have packages, wait until there is sealed brood. (You don't have to use sealed brood but it is better because the bees hatch sooner.) You may want to pull more than one frame and may have to do this several weeks in a row. In any case, in early spring, try to "equalize" your hives. This overcomes the problem of drift.
5. As for killing a queen, every beekeeper does it once. I will never do it again. If necessary, I let the bees do it. They know best.