She was busy with her knitting. Meanwhile, he was dozing by the fire.
Literal
She [topic-は] knitting [with-に] was-busy. That while [also-も] he [topic-は] fire's side [at-で] was-napping.
A two-sentence pair painting a domestic scene. うたた寝する ('to doze/nap lightly') is a common compound for involuntary light sleeping. その間も ('meanwhile, even during that time') connects the two scenes.