Vds voltage significantly high when MOSFET is ON, what could be the reason?

Please refer to the diagram I have attached, the following circuit uses IRF9520 P-Type Mosfet and IRF520 N-Type Mosfet.

I have designed a switching LED, i.e. when we push a button two LEDs in first branch light up when we again press the push-button LEDs in second branch light up and first branch turn off and so on, when we hold the push-button for more than 2 seconds both the branches turn ON and when we again press the push button the first branch lights up with second branch in OFF state. What I haven't shown in the circuit diagram is a push-button that toggles switching between two branches where each branch consist of two LEDs in series. The circuit's pwm is controlled via potentiometer(not shown in the circuit diagram).

I am using two 3V LEDs in series with maximum current rating of 180mAmps in both the branches.
I have decided the Resistance such that max current drawn be 180mAmps in each branch.
Following was my calculation : 
at 100% duty cycle 6V in total drops across the two LEDs so rest of the voltage should drop across the series resistor. Max current rating for these LED is 180mAmp so 12-6 = 6; 6/180mAmp = ~34ohms. So I placed 34ohms resistor in series with two LEDs in each branch.

Now when I connect the whole circuit up few problems arise : 

     1> The LEDs in the branch that has P-Type MOSFET lights brighter than the LEDs in other branch initially at any PWM but at max duty cycle (100%) both shines equally but I'd want both to light up with equal brightness. why could this be happening? I measured voltages across LEDs in both the branches at same PWM by activating both branches one by one at same PWM and the LEDs in first branch with P-Mosfet one had higher voltage drop than the second branch and hence was lighting brighter than the other branch.

     2> Secondly what I expected was, say at 100% duty cycle, there would be 6V drop on LEDS and rest of the voltage drop should be on the resistor in series with the LEDs and a little voltage drop between drain and source but when I use multimeter to check the voltage drops at components in a branch, voltage drops at LEDs according to PWM supplied  but the rest of the voltage should drop on the resistor in series with the LEDs but instead of that a very tiny voltage drops at that resistor and the remaining voltage drops between drain and source. For example if 4 volts drop across LEDs, a few volts(less than 1) drops at the series resistor and the remaining 7.x volts would drop between source and drain. I don't understand why is this happening! At ON state Vds should be less depending on the On-state resistance which from data sheet I found out it to be less than 1 ohm. And this is happening at both the branches with both P-MOSFET and N-MOSFET.

I am assuming it's the problem with my understanding of transistors maybe. Any help would be greatly appreciated.

For starters, Q1 is around the wrong way on the schematic, if it is on the hardware, then reverse the source and drain.
If you are supplying a schematic, make sure all the values for all components are
on it. You don't say that you need to ramp the brightness up and down, so I am not sure why you are using PWM, when on the basis of your comments you are just switching the outputs, the only reason to do so is to use a fixed duty cycle to push the device beyond some of its normal DC operating specs. This can be dangerous during testing, easy to destroy something.
Put logic level drives in place of the PWM when initially testing, make sure the 12V supply holds up when both LED strings are on. LEDs can have a wide spread in output, so you may have to tweak the series resistor in one string to get a similar brightness.
Check the data sheets for the LEDs. Also, if you are running them at max current, heat can be an issue, you must heatsink them properly or expect reduced lifetime.
It is wise to not run a device at any of it's maximum ratings unless you absolutely have no choice.
Make sure the FETs are adequately enhanced with the gate drive you are using.
Put all of the voltages (when the two drive voltages are 5V DC) and put all of the component values on the schematic and re-post it if you haven't sorted it out in the meantime.
Cheers,
Richard

I just realized that but I have put it the right way round on hardware. Also I think since arduino provides 5volts to the gate of Q2, it doesn't fully turns on, could be ,right? I'll make some changes to the schematic and post it again.

Here is the change I have made to the schematic. I have added a transistor to fully turn on the mosfet although the o/p is inverted but i can always code arduino to invert the pwm. Let me know what you think. Also is op amp a good choice to use as a gate driver?

There are a few issues with the circuit, but it should work. The voltage on the NMOS FET should have been OK, I just asked you to check and see that it was. The new circuit should take care of that issue.!
The transistor drivers are not push pull, so the the turn on and turn off times are not symmetric, in this case it won't matter if you are switching with dc, but if your PWM switching frequency is very high, it might become an issue.
As I said, you need to check the circuit with DC, and measure all of the voltages when the two lines from the arduino are in the high and low states, don't use PWM at this stage.
If you need to drive high power FET gates, then there are ICs drivers specifically designed to do it, but in your case they should not be necessary. Don't use OP Amps.
I need to stress this point, put all of the circuit component values on the schematic, including the LED part numbers, measure all of the voltages when the drive from the arduino is in both states(DC), and post that info,
cheers,
Richard