If you're angry about your work being short-staffed, that's not your colleagues fault or responsibility. What are you expecting your workplace to do? They can't force her to go back if she's been signed off- her sick note is evidence enough.
Surely you would understand that if she was at work woth this, she wouldnt be able to just move around or rest when needed- or could injured herself more.
She's been signed off for 4 weeks- does sciatica automatically mean you're bed bound? No. Even a mild case of it is enough to be a reason to not be at work.
At home you can control the strain on youself. Being at work at a desk or on her feet, work isnt great for back pain. If she works on a ward then that's even more reason to not be at work.
Are you expecting her to stop being an adult who not only has to care for herself, but also has to parent and meet her child's basic needs of food, care and emotional stability.
If she was signed off with work related stress would you still think to report her? Or if she told you she had a fever and bacterial infection requiring antibiotics?
When i worked on a ward I've had a colleague that was signed off work for 6 weeks because they had very minor surgery on a little finger. Clearly this person was healthy and active enough to work, did anyone report her for going for a night out?
Being off work sick/signed off does not mean you stay at home 24/7 and life is on hold.