反対 and 逆: an opposite side and a reversed route order
Compare a bus stop across the road with visiting stations in reverse order, checking the reference when opposite directions overlap.
The opposite side of a reference
反対, read はんたい, expresses an opposite side or relation. バス停は道の反対側にあります。 says that the bus stop is on the opposite side of the road.
出口は入口の反対側です。 says that the exit is opposite the entrance. It compares positions without describing an order of entering and leaving.
Reversing an order or orientation
逆, read ぎゃく, expresses a reversed order or direction. 帰りは逆の順番で駅を回りました。 says that the stations were visited in reverse order on the way back.
地図を逆さまに持っていました。 says that someone was holding the map upside down. The map’s orientation differs from a location across a road.
Checking the reference when directions overlap
反対方向に歩く and 逆方向に歩く can both describe walking in the opposite direction in context. Identify the earlier direction against which the movement is compared.
入口と出口の位置を逆にしました。 says that the entrance and exit positions were swapped. This includes a change of arrangement, beyond saying that they are on opposite sides.
Does 帰りは逆の順番で駅を回りました。 describe visiting the same stations in the original order?
Show the answer and why
No. It describes the past action of visiting them in reversed order on the return journey.