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Generally if there is an intake manifold or head gasket concern there is cross contamination both ways. In other words, generally you will have coolant in your engine oil as well. If the engine oil appears milky white on the dipstick or bottom of the pcv valve or oil fill cap... there may be an engine problem. The most common there would be the intake manifold gasket. If your transmission fluid level is a bit low and there is an oily substance in the coolant but none in the engine oil, this usually indicates a leak in the transmission cooler which is internal in the radiator and would require radiator replacement. If the transmission works ok and there is no indication of milky white transmission fluid then there shouldn't be any reason to go into the transmission.
What exactly was your estimate for?
To answer the one part of your question, coolant in the engine oil is not terribly uncommon on those due to an intake manifold gasket leak. Oil in the coolant is not as common. I would want to know if it is engine oil or transmission fluid. The repairs are quite different for each.
So it sounds as if the estimate is for a trans cooler which is internal to the radiator. A radiator and flushing the cooling system and transmission and the estimate is $2000?
That sounds extremely high if that is all they are doing.