I agree that you shouldnt keep a dog that is that aggressive towards your children or your pets, serious injuries could result.
I too, dont think that its the same dog, as soon as I seen the pictures I thought to myself, there is no way. The dog in the first picture is smaller and lighter in color. I dont think the second dog looks dirty and unkept, I think she looks petrified and very unhappy.
.
its unfortunate that this was brought on YT. I think it should of been kept between the 2 of you and the both of you need to decide what is best for that poor dog.
I hope that the 2 of you can get it worked out soon.