A glovers needle is good for heavy leathered skins like beaver and coyotes. Look for the 2 and 1/4 inch size glovers needle they come in a number of different sizes, any smaller and you will have a heck of a time to thread the needle. Next when using a glovers needle if the needle is hard to push thourgh the hide sharpen it.
To sharpen a glovers needle lay the flat sides down and push over a diamond stick or sharpening stone.
Using the right thread is also very important I highly recommend a waxed thread used in sewing awning. you can get it in 30 yd rolls or 180yd rolls in the course thread not the fine.
To close the hole, sew in a circle around the outside of the whole then pull tight and knot a couple of times. When sewing only push the needle in a couple of layers of skin do not go to deep and push the needle right through the skin, you will pull hair through with each stitch and the sewing job will look rough.
For smaller animals like fox and marten use a regular sewing needle just sharpen the tip. Use coat button thread that is heavy and will not break easy. Use the same method as above. If you try using a glovers needle it will spilt the thread will pull out of the pelt.
If you tear the animal across a length then sew back and forth the length of the tear, knot the thread every few stiches so it does not come apart on you.
Sewing holes and tears is important, if a grader sees a hole right away they are concerned. Little hole now but when the skin is dressed big hole and buyer will place a claim.