I too was only advised to feed one breast at a time by my HV - in restrospect, LOTS of things went wrong for me... another story.
But, I also had REALLY sore, bleeding, scabby, unbel-iiieeevably painful nipples. I just kept going though, got the nipples protectors, tiny bit of relief, but then started just bottle-feeding my DS(2) expressed milk. I think your slight discomfort may be nothing like what she is experiencing. I can say quite definitively, the pain I felt was not discomfort.
But, my reasons for expressing and bottle feeding as well were that it gave me some sense of control. Mine was failing to thrive (whatever that is!), and I was panicking he was getting no milk etc etc... plus with a toddler in the house I just felt 'trapped', unable to do anything for my eldest as all I was doing was sitting there with tears in my eyes (from pain and stress). The expressed bottle milk made the feed faster, less painful, and therefore far less stressful.
I felt like me. Maybe your SIL is not actually enjoying the whole process? She is very lucky to have someone like you to be so supportive helping her. I had noone, and gave up at 6weeks. Stupid really, because by about a month in the pain stopped and all the 'elasticity' of my nipples kicked in... I think the stress of it all had got too much by then, and there were too many people around me just saying "oh, just FF if you're so upset". Again, in restrospect, - with myself.
Definitely, if your SIL has the time, or inclination, going to bed for 24hrs with the baby will help. But, I would suggest checking to see how she is feeling generally.
My mind was strong enough to get through the pain, and it being my second (BF til4mths with DS1) I knew the pain would go away eventually), but I think I stopped BFing because of stresses from everything else. The pain was a bit of an excuse to hide all that.
Having said that, when I stopped BF, and switched to FF, my mood changed instantly. I really think it helped for me, stopped baby blues turning into PND. Had I had the right support BF-wise, like you are for your SIL, maybe that would have had the same effect.
But yeah, how is she generally feeling about the whole thing?