A big THANK YOU for making a post where the SIL not the DIL is the problem.
I read your other post a few times and I'm confused about what exactly the problem was with the mascots at the wedding, but as was pointed out, that's a done deal, so don't waste any more time over it.
When it comes to the birth of a baby, the only person's whose feelings and wishes matter is the mother's - she's the patient, after all. If she wants a cast of thousands or no one, not even the dad in the delivery room, so be it. I told my dh that if he annoyed me too much in the delivery room I'd kick him out. The couple isn't required to call anyone enroute, either. Now, the dad can give his opinion on the matters (who's in the room, who gets called and when). If mom so chooses, she can accommodate the dad's preferences and it's no one's business to complain or hold a grudge. It's ok to feel hurt or slighted - we can't really control our feelings - but being resentful is a no-no.
It's possible that your daughter was more than ok with not calling you til after the fact. Maybe she felt she was becoming a mom herself and needed (excuse this poor pun) had to cut the umbilical cord figuratively before it was done literally. If you and your dd call/text every day, it's not outrageous that your sil feels put out. A lot of guys don't understand the intense socializing some mothers and daughters have and feel it threatens their autonomy. He and your dd are adults and need to make their own decisions. He may feel that your constant contact influences your dd unduly - whether it does or doesn't, that could be his perception. Just maybe your dd has played a role in his wanting to keep you at arm's length. Maybe half her comments are preceeded with "Well, I was talking with my mom and she thinks..."
When I was in the hospital with my last child, the booklet with all the hospital info - discharge info, meal info, getting a birth certificate, etc. - specifically said visitors were nice, but even grandparents and siblings should stay no more than 15 minutes. There's nothing wrong with a couple wanting a lot of alone time after the birth of a baby. Your daughter may be uncomfortable telling you to keep a little distance, so she's letting sil take the blame. I know plenty of DILs who would attest that their own DH's aren't thrilled about spending time with his own FOO, but DIL gets blamed.
It's only been 2 weeks. Dont' say anything to your DD. If she asks for help, give it. Try to focus on what you do have. Your GC won't remember who changed the diapers in the first weeks of life. Plenty of gp (parents, too) form healthy, strong, loving attachments even if they have little or no contact in the first months.
Given that your SIL has a very different background and temperment, it may be that he views his behavior as loving and warm. Try to find a way to positively interpret his behavior. My Dh had a grandmother who had something critical to say about everybody. I would have felt unloved if I found out she wasn't criticizing me to other family members (she didn't do it to your face). That's just the way she was.
Good Luck!