Ditto the stance on herbicide...
Organics are great but sometimes there is a purpose for chemicals. This is one of those times.
I tell people all the time that organic gardening is very much like homeopathic medicine. It's great for general wellness and minor problems, but sometimes you have to go to the doctor & fill a prescription. Nonselective herbicides used only in times of need aren't going to be a problem and once dry are pretty doggone pet friendly. That's the basis of Integrated Pest Management -- chemicals only when necessary.
BTW... what's she going to do with the pets while the new lawn is establishing? Seems to me if she's willing to keep them in the house / off the lawn during that relatively long period, another few days for an herbicide to do its work shouldn't be too big a hassle.
One other option... the organic crowd uses "horticultural vinegar" as a nonselective herbicide. You may look into that, but it will probably take multiple applications and prolong the process.
My best advice... give her a price to do it with traditional herbicides, then price it the organic way. Ensure that the pricing will make her rethink her opposition to traditional herbicides
