Yes, your friend is being hormonal, selfish & unreasonable. She is also pregnant with her first baby & last baby, & not yet a mom. Poor thing has not a clue about motherhood, yet (those sleepless nights will come in as a shock for her, won't they?!).
Yes, your kids are sick, but it's only Thursday & with antibiotics, kids normally get better pretty quickly. So, play it by ear.
Also, if you have an able bodied DH, why can't he stay with the kids? Does he work weekends? I think I'd be leaving the kids at home, even if they weren't sick, just so I could focus on my friend & the task at hand. How are you really going to be able to help with the event, enjoy yourself, and care for yourself & 2 kids? Sounds kind of ridiculous & stressful, if you ask me.
Something like this isn't really worth losing a friend over, IMO. I think it would be great to make the effort & surprise her. It would mean the world to her.
Edited - I guess I have more confidence in my husband than most women have in their spouses. It really must be awful not to be able to trust your own husband, the man you chose, and the one you chose to have kids with. Your children will not die if you're not the only ones caring for them. The world will not crumble if you are gone. I highly doubt that your husbands are helpless idiots incapable of childcare. I really just don't get it. I think a good friend would figure it out, personally. You are choosing to miss out on something that is so important to your friend. Just be prepared to lose her.