Simplification of ideal op amp circuit
I'm afraid the simplification is incorrect.
The reason for this is that the resistor \$R_3\$ creates an opportunity for the two nodes to influence each other. The original circuit only allows the output to influence the node between the two capacitances because the output of the opamp is an ideal voltage source (it forces current to flow via ground or a supply voltage). This is why buffers are typically used: to avoid the output influencing the input.
You will have no choice but to include an ideal (voltage-controlled) voltage source on the other side of \$R_3\$ that has the same voltage as \$V_2\$.