Hey Chantsy I can certainly understand how frustrating this is for you. Way too much work to try and always have dual events.
Birthday are a huge issue and almost always result in angry emails, blame for lack of inclusion (although we always invite her), and other stressors.
What are some of the other stressors?
You say you will have a big party for your husband. Is there some way to have one parent come early (and leave early) and the other parernt come late (and leave late)? If your dad and stepmother have been to multiple events in a row, one option would be to invite your mom to this one.
Is there some way to work out some method of alternating attendance? Your mother to one event, your father and stepmother to next event. When one side doesn't attend, they can offer something that they host on a different day, if that is mutually agreeable?
I'm sure the birthday situation is only one of many issues with your mom. If you would take the personality disorder out of the equation, it is common for divorced people to NOT want to be at gatherings with their ex (especially with the ex's new partner in attendance). Sometimes, I don't think it even matters who initiated the divorce.
You can continue to invite both parents and ignore the nasty emails from your mom. You won't likely change your mom. No matter what choice you make, she will likely have something to complain about, unless she is the one to attend every event without your father and stepmother.
Sadly, no perfect solution.