Is There A Better Way Than Straining To Clarify Lard and Tallow?
When I have rendered lard, I have generally just heated the solids with just a little water at the bottom of the pan over low heat.  I never let it get to a boil, and this does take a long time.  When the fat is all liquid, I pour it through a strainer lined with cheesecloth into a second vessel, then pour the strained liquid into jars.  I have not had issues with impurities - my rendered lard is very clear and white.  I have found straining to be very effective.

You don't mention the amount of heat or exact process you are using, so I can't speculate as to what your exact situation is, but it's possible you are trying to do this over too high heat.