Loosing coolant no leaks I can see this takes my kids 2 scho

Please help me! I bought a 1994 plymouth voyager with 114.000 miles on it, about a month ago 2.5 l 4 cyl. It is using about a gallon of antifreeze every 2 weeks, or less. Can find no leaks anywhere, the thermostat was missing so I replaced it last week, and same thing. Someone told me to let it idle with te radiator cap off to burp it, but after a min or 2, it starts overflowing, so I have to leave the cap on it, but the coolant is not in the oil, or vice versa, and its not blowing it out through the overflow, that I can tell, any ideas? It runs great, except when ideling, it will run rough for about 20 seconds, then fix itself, done complete tune up, and idea what that could be also? Thank you soo much in advance, all advise welcomed. Chris