Since the kids are different ages, she'd have to dump them off at two different times, and frankly, the kind of woman who would pull this with two different children isn't likely to come back to the same kindly neighbor with the second one. She's more likely to just leave them in a parking lot or something.
Also, in most states you can only dump an unwanted baby at the designated places before it is a month or so old. After that they will try to find and prosecute you. Some places didn't make this distinction and there ended up being a few cases where parents dumped their unruly teenagers off at hospitals and such.