NADINE- your problem is due to Galvanic Corrosion. When you put a brass or copper plug or fitting into an aluminum radiator, and fill it with an electrolyte-(coolant), you get a "battery". The galvanic corrosion will eat the aluminim in the radiator as a sacrafice to the brass plug, and cause problems such as you are having, as well as leakage.
I am sorry to say, the radiator is shot. if those plugs have been in there any longer than a month or so, the radiator is structurally weakened, and can fail at any time. I have seen 5 or so radiators killed over this same mistake in a matter of months. (ONE OF THEM MINE! didnt even think about it...)
You can CHANCE drilling it and repairing it, but how long it will remain leak free after repair may not be worth the work involved to do it twice. One good way to tell if the radiator has been strongly affected is to pull off a hose, and look at the end of the aluminum in/out necks on the radiator. If they have turned dark gray or black where the alumium was exposed, toss it.
If you happen to have an aluminum plug that is causing the problems, it sounds like the typical aluminum 1/8 pipe problem...they ALWAYS want to strip out when you remove them... and get stuck. you have to drill them and tap them to 1/4 to get rid of the problem. 1/4 does it rarly, 1/8 is very frequent.
NOTE: NEVER, EVER use a brass or copper plug/fitting in an aluminum radiatior. ALWAYS use Aluminum plugs and fittings, or second best, Steel.