Just use a much more simple example to think about this phenomenon :
If you walk throug an airport terminal and step onto one of those typical conveyours, you note your sudden loss in walking speed due to a change in reference system speed.
Now change direction, and walk back against the conveyours movement. You don´t need different forces compared to doing this on solid ground, all that makes it feel strange, are optical illusions. Try it with your eyes closed, you will notice no difference between doing it on a conveyor or on solid ground.
It is the same type of optical illusions that trick you if flying the circuit in strong winds with a light aircraft.
Even simpler : let´s assume you live close to the equator, then you are traveling eastbound with 1666 km/h (40,000 km in 24 hours). If you walk eastbound and change your direction 180°, your speed relative to the center of the earth has changed from 1670 to 1662 km/h eastbound, but if feels like just changing from 4 km/h eastbound to 4 km/h westbound.