I've done this before. Sending packages to the other side of the country, with a slightly weird (to me) address--I wanted to make sure it got there, and if you wait too long to check and it hasn't arrived, the trail goes cold pretty fast.
I admit it can be awkward, though. Maybe you could drop her a quick email and say, "Hey, UPS tracking said you received the package I sent, could you just let me know if it got there safely? I know you're super-busy with the new baby so I didn't want to bother you, but one of the items is fragile and I want to make sure it made it there okay." Throw in a smiley face or something.
I actually think it's better
to do this right away, like as soon as the tracking says it was received, because no reasonable person is going to expect to receive a TY note that fast (though I guess some people might demand a call or email), so it lends more weight to the idea that you're just making sure it got there.
Story time. Every year my friend on the other side of the country and I exchange holiday gifts. She is notoriously slow at TY/acknowledgements, which really bugs me because she has a weird address--think Harry Potter's "Cupboard Under the Stairs" or something. She's slow about communicating in general--responding to emails, sending me my
gifts (once I got them in February), etc., so it all goes together.
One year I was, I admit, overboard about asking if something had arrived. I think I sent her three emails asking if it came (three because the first two had received no response). I was complaining about it to someone else, saying, "I'm not even asking for a TY, just please tell me if it even got there!" Finally the friend responded by email, and it was literally just, "Yes, it arrived fine." No word of thanks then or later--but I guess I had kind of "asked for" that, right, by saying to the universe that I just wanted to know if it arrived.
After that, I decided not to worry about it so much. I send something to her (increasingly, electronically-delivered gift certificates), I tell her by email that I've sent it, and I let it be her
issue as to whether it arrives or not. (If you're wondering why we still exchange gifts... I'm okay doing that. I've dialed it down over the years in terms of $$ and I wait for her to initiate the idea now. One of these days she won't mention anything about it, and in that case I won't give her anything, either.)