Joints on any type of dance pole can get tight or stuck, especially when the dance pole has been installed for a long period of time. Temperature fluctuations, daily use, and other humidity factors cause metals to expand and contract which can make parts feel stuck or hard to get apart.
For screw together type dance poles, the best tool to use is a rubber strap wrench to loosen the main pole pieces without damaging the chrome. The straight peg shaped tool in your original dance pole tool kit is the typical way to loosen the pieces and can be slid through the holes in the dance pole extensions allowing you to get better leverage on the pole to both tighten and unscrew the parts. Be sure to slide the peg through BOTH opposing holes in the extension pieces. The rubber strap wrench option is easier than the pegs. Alternatively, you can use some tacky pole dance grip gloves (or one of those grip pads that are commonly used in kitchen to loosen the lids off jars) to loosen the main pole pieces without damaging the chrome. Football gloves or any glove with silicone on the palms has been reported to work well. Enlist the help of a friend and have them help you unscrew the pieces by holding onto the opposing pole part. Working together by twisting the joints in opposing directions at the same time makes things easier.
For X Joints found on X Poles, it's common for the hex key in the joint to get stuck, if you hear a pop after finally getting the hex screw to loosen, it's ok - that noise happens when it's stuck or a little tight. Once the hex key is loosened, use the same type of techniques mentioned above to get a better grip on the pole to pull the joint apart. Sometimes having a person hold on to one end while you pull on the other makes a world of difference.
WD-40 can be used to loosen stuck joints and threads as well. Just remember to promptly clean away any WD-40 on the surface finish of the dance pole because it's very slick. It will cause you to loose grip on the pole.
We understand stuck joints are no fun, but they will come loose though, you just may need to get some better tools or the help from someone with strong arms : )