I had almost this identical issue. I really feel for your SIL! I never developed mastitis, but I would get one of these clogs every month or so. What worked for me is to put a wet washcloth on my nipple, and then sit with a hot pad over it for a long time. I would sit there while watching TV for a few hours, massage it and then try pumping. I even slept with it like that and would try to pump while it was still warm. It might take a few tries, but this always worked for me.
If she is weaning, she might just wean from the boys but use the pump in the meantime to avoid clogs. It is a lot easier to wean from the pump when she needs to, if that makes sense.
I hope she gets some relief soon!
C.