Should I sand between coats of polyurethane when finishing a table

You're spreading the mud out over a progressively larger area so that instead of a small but sharp bump (or dip) in the middle of the joint, you have a much more gradual bump (or dip). That way, any irregularities in the surface are much less noticeable and can be easily masked by texturing.

Pine is a difficult wood to stain under the best of situations. Pine has areas of different density, color, and resin (pitch) content. Using a product like Minwax prestain helps a bit. Follow the timing instructions carefully when using a pre-treatment. Little tips: i like to apply a liberal coat of oil based stain with a sponge brush. Let it set a few minutes, then rub it in and evenly distribute with a lint free rag. As one rag becomes saturated with stain, I use a second drier rag to finish the rub in. The wetter rag is great for distributing the color. You don't want any really wet stain remaining on your wood after the rub in. Once you get to the urethane, sand lightly between each coat with 220 grit paper to remove any dust bumps. Remove all sanding dust with a slightly damp cloth, let it dry and apply next coat. Again, I prefer a good grade sponge brush, but a good grade regular brush for oil/urethane works good for appling the urethane. Remember, thin coats, and sand between each coat.