What is good to use to soften and remove cuticles?
Wash the dishes without gloves, then attend to your cuticles using an orange stick and a sharp pair of clippers to cut the bits to be removed. Never tear or bite off cuticle, that will leave an ugly mess.
There are expensive creams and other products out there that you can blow a lot of money on, but simply attending to your cuticles after washing you or the dishes is the best and least expensive way to keep cuticles in line.
Follow up with a bit of an inexpensive hand lotion, and you'll have lovely nails and hands.
Massage Vaseline into your hands and nail. I do it while watching TV. The cuticle softens after a little while.