Having been a professional auto mechanic for over 34 years, I've had quite a bit of experience with exactly the problem you now have. No, you are not supposed to mix the 2 types of antifreeze - it will definitely cause severe problems with your cooling system but not in such a short time. I have replaced countless engine parts that have been deteriorated from mixing the dexcool with either etheylene glycol or propylene glycol antifreezes. It seems the mixture really attacks aluminum parts - eats them up. Have replaced many intake manifolds, timing covers etc. - expensive parts because an owner or inexperienced service person mixed the two, but this takes a little time to occur. You should thoroughly flush the cooling system and replace with one or the other types of antifreeze. In automotive experience, I have seen no better long-term service from using dexcool over the other types of antifreeze, the systems don't seem to stay any cleaner or protection last any longer. The procedure I would use to flush would be to drain the system, remove the thermostat temporarily- no need to try and seal the gooseneck at this point just reinstall the bolts for now, disconnect the upper radiator hose at the radiator and lay it aside safely away from the fan. Use some plastic cable ties or such if necessary to keep the hose away from moving parts and to direct the water in a desirable direction. Fill the radiator with clean water until it runs out the neck where the hose is diconnected. Leave your garden hose in the filler neck of the radiator running low and start the engine - the water will be running constantly out of the radiator hose with the thermostat removed. Adjust the garden hose flow to keep the radiator full/ overflowing while the engine idles and purges the system. This will be sure to get every last bit of the bad mix out of the block etc. - simple draining will not do this !! Once clear water is coming out of the hose, you can stop and drain the water out, reinstall the thermostat & hose to the radiator - recommend a new thermostat while there and fill with the proper mix of whichever antifreeze you choose to use. Even though your system drain may be the lowest point, there are still many areas in the engine that can hold several ounces of the bad mix and that's all it takes for the chemical reaction to take place that will lead to big headaches later on. Good luck !!