Between a Rock and a Hard Place

My mom is turning 60 soon, and while this will not be taking us to Mexico, we will be having a party. Her everaccomodating Beau has spear headed this project with the help of my sister and I. Earlier this summer the planning began, starting with the guest list. We kind of left it up to my mom who she wanted to celebrate with, seeing as she does not handle birthdays well. When she emailed her final cut my sister and I were kind of surprised to see that my in laws were left off the list. Now in some families this would be a normal thing, but we roll a bit differently. Tim's family is small, consisting of 2, sometimes 3 people, so adding them to the guest list is not like adding 15 people. While my sister and I thought it odd to exclude them, we respected her wishes. I did ask, but my mom said no way.
So the invitations go out, and my mother in law starts asking questions. What are you doing for your mom's birthday? Should we plan something? Why did Judy make those dresses? Rather than say "We're having a party, you're not invited" I just said nothing. I played dumb, took the invitation off my fridge, and avoided it, but that could only last so long. I finally said something to my mom about how uncomfortable it was, and after a few days she relented and told me I could invite my mother in law. Well how the hell do I do that?
Send her an invitation, right? Well, they have an RSVP by date on them and I don't want her to think that she is an after thought because to me she isn't, but she was to my mom. So I kind of eased into it and gave her a heartfelt verbal invite, giving her only the barest of details so as not to make her feel like she was an afterthought (which she was, but not mine). Seeing as she is not a total moron, my mother in law kind of figured out that this was not the spur of the moment event that I may have led her to believe. (ok, I did lead her to believe that, but what was I supposed to do?) Now her feelings are hurt, as they should be, and I feel bad for her.
She now doesn't want to come mostly because she feels like she is not wanted, but partly becasue when she asked me if my father in law was included in the invite I told her that he could only come if he wasn't a schmuck (he tends to stand in the corner looking crabby, making it obvious that he would rather be 100 other places than where he is). I think it is more the former than the latter, so what do I do?
I want to apologize to her because I genuinely do feel bad, but that would be throwing my mom under the bus, and really would she believe me?
So is it better to play along and let her feelings be hurt, and inevitably be mad at me thinking that I excluded her or tell her it was my mom's fault and cause a rift between the two of them? Which one will screw me less in the end?