NTA

Not even for giving your sister an invitation. I would want that invitation, even if my world was in the ICU, because I love my sisters children too! If I were the niece-- the 20 year old niece-- I would hope someone would call so I could see my little cousin blowing out her candles! I would never want to take that from her... bit I'd jokingly ask for a piece of cake!

The only way I can readily fathom you being TA is if you sent her an invitation without ever acknowledging your niece's condition, or your sister being understandably fraught. Have you taken the younger set so she could be at the hospital? Have you gone to visit if it's allowed? Have you dropped off meals? Because if you've been involved... you've done nothing wrong. Every 4 year old deserves to celebrate their birthday. It absurd to confuse that with also loving your niece.