a three piece gadget sounds suspiciously like a cleaning rod which was re- labelled and sold as a ramrod... the advice Ghettogun gave about getting a range rod is good- you should get one and a spare, just in case. Look for pins where accessories meet the rod: the tips should have both glue and pins- glue alone will fail, and Murphy's law dictates that this failure will happen as you're trying to reload. The the Boone & Crockett buck walks by. He didn't flip you off 'cause they have no fingers.
grab the rod no more than eight inches above the muzzle, and don't put your hand on top of the rod (there was an incident where an accidental discharge happened as the shooter was loading. there was no cap on the nipple, but the rifle went off as the ball was being seated. if the shooter had had his hand on top of the ramrod, as opposed to just having his fingers around it, it would have blown an impressive hole all the way through his hand). Of course, never pour from the horn- always use a measure.
on the don't- run- with- scissors rant, don't stand directly over the muzzle at any time, and don't blow into the muzzle (never understood why anyone would do that, but i've seen it done) a short starter shouldn't snap off as you described: i'd invest in a replacement from a reputable manufacturer.
these problems are bumps in the road- overcome them and you will make a boatload of good smoke!