As we know V=Ir so why potential difference do not change even after the current split
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Answer:
The understanding of ohm's law is different. It always says that for a fixed length of wire, the voltage across its ends is proportional to the current flowing in it. And the constant for this proportionality is what they termed as resistance.
Also note that current and resistance are inversely proportional. So v is proportional to I and v is proportional to R is a wrong assumption because V proportional to R is at constant current. And V proportional to I is at constant resistance. Don't try to combine these 2 equations.
V is proportional to I. That means, V/I is constant. That is resistance(R) . So now think like for a given resistor of resistance R, the ratio of voltage to current is always constant.
It is not that voltage and current don't change. Even if they change their ratio would be constant