It sounds like hormones are on the loose! A good heart-to-heart with her ob/gyn or primary care doctor would be great right about now, I suspect.
That being said...been there, done that! I had our son at 36, just a couple months from 37. Although some women might be wiser and more relaxed in some respects as an older mom, it also does a serious job on your psyche and your energy levels! If she's been a professional woman up till now, she might be feeling like "I'm intelligent, I'm mature...why is this soooo hard?!"
Some of us older mom's are too informed for our own good. That may or may not be the case with your SIL, but I'm guessing I'm not too far off the mark. I can remember beating myself up emotionally, quite often, because I felt like I should know how to do...XYZ...already. Why? Because I'm female? Because I was older? Regardless of age, it's all a learning experience.
My husband is 6-1/2 years older than me, so he was 43 when our son was born, and we both were reduced to driveling idiots sometimes when it came to parenting! I can laugh about it now, but I cannot tell you how many arguments we had about the "right" way to hold our son or to nurse or to do just about anything else. It could have been a comedy routine! We were pathetic! However, in the moment, it was devastating.
There is something to be said for youth and ignorance when it comes to having a new baby! All kidding aside, energy, hormones and sleep-deprivation are probably doing their dirt about now with your SIL. Plus, she probably needs to verify that her blood sugar levels are all up to snuff as well.
See if she has access to a visiting nurse or lactation consultant (it took me a month or more before I got the hang of breastfeeding); be there for your SIL; help her see the humor in this new adventure; remind her that it is a learning experience (not everyone knows intuitively what to do); help her get out and meet some new moms; and help her to get some exercise at whatever pace she is able (it helps the endorphins kick in).
Did she have a C-section? If so, that's particularly a drag when you're older, too. It took me a full 6-8 weeks or more just to be able to get to the point of being able to enjoy our little one without some pain. The older you are, the longer it takes to heal! Meanwhile, I feared I wasn't bonding appropriately with our son while my husband was bonding wonderfully! I was feeling deficient in all sorts of ways...whether real or imagined.
If there is any way to help her see the humor and joy in the midst of this all, it may go a long way to recovery. Of course, that can be a fine line. One person's humor might be another person's breaking point. Be gentle with her and remind her to be gentle with herself as well.
If you can make meals for her or have someone help with cleaning, you might be surprised how that lifts a person's spirits. Or just being there sometimes is the trick.
Best of luck!