There isn't any physical reason why there should be more lateral motion (side to side or lateral yawing), as the couplers really don't restrict twisting motions like that.
I have no idea how you come up with that concept. It used to be said a lot that a train is like a dog. it wags its tail. That is, the back end of the last car will wobble side to side more because it is not coupled to anything behind it which does help it stay centered.
What you might feel is a rougher ride forward and backward (i.e. lurching) as the train crests hills and dales--every time the train goes uphill, it stretches, and every time it goes downhill, it compresses.
This effect is minimal to completely imperceptible in the normal passenger train consist. In my college days riding Southern Railway's piggyback trains with a couple of coaches in the middle that passed for their passenger train on western lines, slack action could be quite noticible, but then usually you had 10 to 12 head end cars ahead of you and 10 to 13 piggyback cars behind you. On the other hand, on those days that the train was short, for some reason the Sunday night trains tended to only have 3 to 4 head end cars and no piggyback, there would be no noticible slack action at all. Being in the first or second coach made no difference at all in front to back motion, wheter the train was long or short. What was noticible on the days that piggyback was absent was the extra side to side motion of the last coach. Before it was dropped, the sleeper was always the last passenger carrying car, so you definitely got rocked to sleep.
Passenger equipment may have some cushioning in the drawbars (I can't recall specifically--I'm pretty sure the couplers have anti-jackknifing extensions or something, but I'm not sure about cushioning or anything to reduce the slack), but a well-run passenger train with a good engineer who applies power and brakes at exactly the right times can make the ride as smooth as silk. (On the other hand, a bad engineer can throw you around and cause injuries...just ask old-time conductors and brakemen who used to ride in cabooses, widely considered the deadliest place to ride a train...)
Sounds like what you are thinking about is tight-lock couplers. These couplers have a protrusion opposite the knuckle that fist into a pocket on the coupler it mates with so they cannot bypass vertically. This si primarily a safety feature to help keep the cars lined up in case of derailment.
The "throw you around" I assume to mean the forward and backward motion due to slack action. Yes there is true skill in minimizing this.