Hello and thank you for using this service!
I am sorry to hear about the problem you are having with your fridge :(
Let's work together to find out what is wrong :)
A vibration sound sometimes can be as simple as a tube touching back in the compressor compartment. In order to check that, you would have to remove the back cover while the machine is making the noise and touch the various tubes in the back in an effort to locate the source of the sound. The fact you say you can quiet it by pushing on the door would lead me to believe that is the case.
The other issue is french door refrigerator are very fussy about being level and sometime just adjusting the leveling legs or setting the "locking feet" located on the bottom front corners of your fridge. That would be the first thing I would do if I were at your home.
Check your manual on leveling procedures and the next time is starts making noise, try adjusting the feet and the locking feet to see if that will correct it.
If that does not work, then remove the back cover and see if you can locate by touch where the sound is coming from.
Issues like this sometimes just take time to locate, so be patient and you should be able to find it.
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Have a great day!