Hmmm. I think it would be much easier to make a simple structure to support the plastic, but if you want to do it with pressure...
Brief tutorial on pressure sensors:
All pressure sensors have a diaphragm which flexes back and forth depending on the pressure on each side. The amount of flex depends on the difference in pressure across the diaphragm and is typically measured with a strain gauge bridge. Sometimes the output signal is the bridge voltage (i.e. 0-60mV) and sometimes it is amplified (i.e. 0-5V). There are other ways to measure flex and other types of output signal, but voltage is the most common and simplest to interface to Arduino.
Most sensor outputs are 'ratiometric'. That means if the supply voltage is 10% high, the output will also be 10% high. The Analog to Digital Converter in the Arduino is ratiometric to the ADC reference which is by default, the 3.3 or 5V supply. That means if you connect the Arduino power to the sensor you will not have to worry about differences between the sensor voltage and the ADC voltage.
Absolute Pressure Sensors read the pressure of the ambient air or the pressure at the port if there is one, relative to vacumn (0 pressure). minimum output voltage = perfect vacuum.
Differential Pressure Sensors read the difference in pressure between two ports or between the port and the ambient pressure (see gauge below). minimum output voltage = same pressure on both sides.
Gauge Pressure Sensors read the difference between pressure in the port and ambient. minimum voltage = same pressure at port as ambient air pressure outside the sensor.
Sealed Gauge Pressure Sensors This can actually mean 2 different types of sensors. 1 has a sealed membrane between the reference side of the diaphragm and the outside world so it acts just like a Gauge Pressure Sensor above. The other reads the difference between the port pressure (or ambient) and a sealed cavity inside the sensor that has been pressurized to nominal air pressure, usually at sea level. They can also be absolute pressure sensors with nominal pressure subtracted from the output signal. minimum voltage = ambient pressure is the same as nominal air pressure.
Vacumn sensors operate the same way, except they can read 'negative pressure' i.e. the pressure is lower than ambient air pressure. Some differential pressure sensors can only measure when one port is higher than the other; some can measure if either port has higher pressure.
For your application, you will need a differential pressure sensor with one port connected to the outside and the other port to the inside or a gauge pressure sensor with the port monitoring the pressure outside (assuming the sensor is inside. It can also be done with 2 absolute pressure sensors (one inside and one outside) and subtract to get the differential pressure.
Plastic doesn't weigh much so you need a very low pressure sensor. Probably much less than 1 PSI differential. You will control the fan to keep the inside pressure higher than the outside pressure.
The greenhouse will have to be very well sealed. Everywhere. Every seam, every joint.
It will probably need some kind of airlock or you will lose a lot of air every time you open the door.
I don't know if regular fans are good for maintaining constant pressure. A regular ventilation fan will probably have too much leakage around the blades and will probably overheat when there is very little airflow around the motor.
The fan will need a damper or some kind of 1 way valve or air will flow out anytime the fan is off.
This will probably use a lot of electricity.
Good luck if you go ahead with this project,
Steve
...will be very helpful