You don't measure resistance with power to the circuit. It will give a false
reading and can even damage the meter. Resistance can be found by ohms law.
R = E/I, Resistance = Voltage (across resistor) / current through resistor.
Also, your thevnin model is inaccurate; all signal sources, including
bateries and power supplies, have an internal resistance.
Furthermore, you should say "parallel" and not "series".
Putting an ohmmeter across a battery is a good way to damage or burn
it out.
However, try turning off the power supply while the probe is connected
to the load. Then turn on the power supply. Your reading should still
be close to the actual resistance of the load. This is because the test
current is already "being pushed" through the load and ohmmeter's
volt-meter will be reading this value of the test current. The source's
current will not be able to push more current into the load.
Give it a try.
Methinks you know little of electronics and have even less practical
experience.