Very gently, OP, I am not sure SIL wants you at this party. You don't invite people to parties out of obligation but because you would like their company. Her reasons for not inviting you might be benign: there's a lot of you and it would make too many people, she just wants her family, she has another idea about how to spend this special day or she doesn't think it's such a big deal.
You sound like you disapprove of SIL. People attending your events is unrelated to you attending theirs. It doesn't follow that because you invited her to your child's party she will invite you to hers. We can all invite who we want to our houses as we see fit. Nobody owes you an invite or can be compelled to attend.
I hosted on my DD's first birthday: we had tea and cake and a houseful of family and kids from baby groups with their parents. It was nice but added an element of stress to the day. I resolved that next year we would go out for dinner on her actual birthday so someone else would cook and I could have a celebratory glass of wine. Any other celebrations are held at another time. This has worked for us. Maybe your SIL is wiser than me and has worked this out ahead of time.
OP, I think you are holding onto all this a bit tightly with your interpretation of the transactional nature of relationships. Nobody owes you an invite and equally it isn't a terrible reflection on you as a person/family if no invite is forthcoming.
Also, if they are cancelling on a regular basis, make sure to invite others who will turn up. You can't force these things.
I am not a fan of last minute cancellations personally and try not to do it, but equally I don't give too much thought to the cancellations of others. I might not only invite them the next time so the event goes ahead though and it would be taken into account a little in the future, without offence being taken. We all have people in our circle who are more likely to cancel. Anticipate it and just enjoy their company if they come.