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Originally Posted by BobK  In (a), she's out (away from home), writing in a cafe; her daughter is presumably at school/nursery. I don't know why the writer says 'asleep' there.
In (b), she's doing (a) but also - even while at home, where's she's usually distracted by her daughter - taking advantage of that bit of peace between her daughter's bedtime and her own, to do a bit more writing.
I would expect to hear (b) more than (a) - because I don't really understand (a). 
b |
I assumed her daughter was with her in the cafe and slept in the stroller.
Sentence (b) is problematic because it sets us up for a second independent clause but delivers a subordinate clause.