Can someone please tell me how it is realistic that two level two infantry at 95% get defeated by one level 1 armored car at 88%
To build, you must first destroy.
An Armored Car at Lvl. 1 regularly deals 2.0 damage when defending against/attacking infantry units, but since it was in the plains, it was boosted by 50%. This allowed it to deal 3.0 damage to your infantry each time, and boosts its hit points up to 22.5 (originally 15).
An Infantry at Lvl. 1 regularly deals 1.0 damage when attacking armored vehicles (tanks, armored cars, etc.), they also have no boost. Since you had 2 of them you would deal 2.0 damage to their armored car each round. You only have 15 hit points.
Without considering the condition of the units, you would need over 11 rounds to finish the armored car, while the armored car would need 10 rounds to finish your infantry units (condition points do affect battle). This would allow a close win for the armored car.
This example is not entirely accurate because the damage dealt is reduced each time based on the condition points.
Other things to consider helping your enemy win here may be their fortifications, or if it's one of their core provinces.