I think your SIL should have a talk with her son and DIL. There seems to be some hurt feelings, some assumptions and a lot of miscommunication. I am a Nana and if I was always calling to visit my DGD but was told that it was inconvenient I would not let it go at that. I would ask when it would be convenient. I would also ask if I could help by watching the baby so Mom and Dad could have a meal or movie out. It seems to me that no one asks the proper questions.
Can I visit?"
"Not today, it is not a good time."
"Okay."
Is that it? No conversation about when time together is possible? No asking how it is going and if there is any way to help? In 4 months no one has probed to find out why only two visits? If I knew that my DDIL has had nights without sleep I would not be waiting for an invitation, I would be on the phone offering to sit with the baby so she could have a nap, get her hair done, go shopping or just take a bath. I would ask if I could bring meals, pick up groceries or run errands. No way would I just let her go on exhausted.
Not everyone has the social skills to extend invitations and not everyone knows how to ask for help when they are tired. I would have no problem asking my DD if they need help or taking the baby when they visited me. If my DS and DDIL have a child I hope that I have fostered the kind of relationship with my DGD to enable me to ask the questions I need to in order to find out how best to visit or to have them visit me.
I am close to the young couple down the street and take their baby for a little while whenever I can but what I found was that when she and the little one visited she was really here for a little break. Sometimes just taking the baby, making Mom a cup of tea and the time to just sit back knowing that the baby is cared for is the best present. It took a little effort on my part though, this new Mom had no idea that I was happy to help, as much for or perhaps more for me as for her.