The oil cooler sits on top of the EGR cooler and oil passes through the EGR cooler to the block. Hence oil could get into the coolant via the EGR cooler, but only via the gasket between the EGR cooler and the oil cooler or between the block and the EGR cooler.
Was the previous repair to the oil cooler? If so then it is possible that that repair wasn't done properly, eg the screws weren't properly tightened, and therefore perhaps the previous repairer is liable for this repair.
Edit: Your vehicle won't be driveable so would have to be transported elsewhere.
MY21.5 L405 D350 Vogue SE with 19s. Produce LLAMS for LR/RR, Jeep GC/Dodge Ram
VK2HFG and APRS W1 digi, RTK base station using LoRa
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