My home is next to Istedgade, 5 minutes walk from the central train station. You will love it because of the atmosphere, it's in the centre and the absolutely amazing balcony.
Your children are so very welcome, if they can sleep in the living room on the sofa bed.
Pls also remember to enjoy the courtyard which really is an oasis in the middle of always living Vesterbro. And Vesterbro is the place in Copenhagen you wanna be, no matter your taste :-)