... That is, if 'eintrichtern' is the best translation. My bilingual dictionaries, however, don't match up these two expressions, so it may not be quite the same, though the similarity in metaphor is tempting.
To me the difference is that 'drum sth. into so.' emphasizes repeating it over and over, drilling a concept again and again as a teaching technique, but not necessarily unkindly; whereas 'force sth. down so.'s throat' emphasizes insisting that they listen against their will, forcing it on their attention in an impolite or aggressive way, but not necessarily by repetition.
Oxford-Duden adds 'cram,' which is also definitely worth adding, higher up my list than 'ram.' And it mentions 'shove,' so it's probably not just AE, sorry.
You can actually speak figuratively of force-feeding someone facts, information, knowledge, etc.; that might be another useful similar expression.
CM2DD, was the name of your English source the thing you perhaps meant to paste? (-;