She's being a moron and lying to your son, she's in the wrong and she's screwing him up.
But you can go some way to allieviating the problems, you need to sit down with her AND your son and explain who the other woman is, explain that no matter who you end up with she's his mother and even if you remarry or whatever, no one will take her place, etc, etc.
She'll be feeling insecure and be worried probably being the cause for half her behaviour.
But its also unhealthy to only see your kid while "out" doing things, you need to be a dad, which includes sitting around watching tv, or mowing the lawn, or having dinner at home, and helping him do his homework and so on. Its unhealthy to take him out every day and she should see that its bad for HER if you're the "fun parent" who never has to discipline him, or make him do his homework, or brush his teeth, or anything else. She doesn't want your kid thinking of her as the boring tyrant at home and you as the guy who only takes him out to do fun stuff. Its bad parenting, and its worse for her as she'll always seem like the mean one.
If she fails to listen to reason, fails to let you spend real time with him at home rather than always out doing things, then she's just a moron and I'd get a lawyer involved asap.