If you are going to keep the dog, you have got to train it. A lot of the reasons dogs are so difficult and that so many of us find them unsavory and downright unwanted is because of pet culture that doesn't train them. It sounds like this dog has no boundaries. Frankly, even if you train it it may not work, but it is out of control right now. You can't live like that.
I hope you find a solution that works for you, not what people try to shame you into doing--love dogs without perspective.