No Invitation drama

We send out our LO's 2nd Birthday invitations a couple of days ago. Yesterday my MIL asked me if we send one out to my SIL and I said no. She wasn't happy about that but said she understands. So than we get a phone call from my husband's aunt, saying she ran into my SIL and started crying for being upset. It wasn't clear if she was upset because she didn't get invited or something else. The deal is my SIL has a falling out with her brother, she chose not to speak to him, making all family gatherings awkward and uncomfortable. When she had her Birthday Brunch, she invited her brother with his girlfriend and her parents but not us. She plays NO part in my child's life, in fact my toddler doesn't even know who she is. So we decided that we are going to have a fun day with people who care about her!!! But, now my husband is cracking and feeling guilty for excluding her. This isn't fair to him or us, when she decided to not invite us, we didn't cause a scene or make other people put pressure on her. SIL is playing victim card and I'm really tired of especially his mother guilt tripping my husband for her.

In the end of it all, it's our home and our baby's day and it's not about anyone else. Do I discuss this issue with my MIL? Should my husband?