I think you may be using two-way stretch fabric, instead of four-way. I had the same problem with a fabric tail - I couldn't get it to bend at the knees without tearing! I made my fabric tail like a cone with only one seam down the center back...what I did was open that seam and insert a 4 inch wide piece of the same fabric, but this piece was cut perpendicular to the rest of the tail. The main body of the tail stretched around, but did not stretch up and down, and the additional fabric gave me enough ease because it stretched in the lengthwise direction. (When I put in this piece, I took in the main body 2" on each side to keep the fit, the seams disappear into the velvet.)

Does that make sense?

If you can find velvet spandex, you don't have to worry about it as it stretches in each direction, but it's VERY expensive.