My Great Dane is always Barking?

My partner left me with 4 kids and his Great Dane! I have never turned an animal away in my life and I am not going to start now as my ex suggested I 'get rid of the dog'. I have obviously become attached to the dog but the only problem I am having with her at the moment is when I let her out the garden in the morning she starts barking (this could be 7 am on a Sunday!) then she does it throughout the day and a great dane's bark is SO loud. I obviously take her out at least once a day for at least an hour but with 4 young children, 2 in a pushchair, walking the dog is a nightmare especially when she pulls but I am persevering and trying to train her myself! Its just the barking I'm worried about as I don't want neighbours complaining. Any suggestions please?