Hi I have a mobile home that has a 100 amp service in it I think it is a Sylvania and a 200 amp service square D on a pole in the front yard. The 200 amp service has a 100 amp breaker that is wired to the garage and there is another 100 amp breaker in the service for a building that was removed from the property. My question is can I run a 2-2-4 to the mobile home under ground and hook up a grounding rod to the mobile home box

No, since the Main Breaker is at the pole, the feeder must be 4 wire to the home, for the two hots, one neutral and one equipment ground, with the ground rod driven at the pole grounding both the neutrals and the equipment grounds. Check local codes, some jurisdictions require two ground rods.

There is a 100 amp breaker at the box in the mobile home also

That fact does not matter. All grounding must be done at the first Main Disconnect.