D.B.
Kids lie for a lot of reasons. No reasonable adult (like your brother's fiancée) would take the word of a 5 year old. So saying she's causing huge problems is probably taking it a step too far.
Her dad and grandmother need to understand that kids lie for attention and it really should be obvious to them that the kids' bodies and clothes indicate that accusations about no baths or laundry are absurd. If they are keeping the kids from you, there's something else going on. But again, no sensible adult listens to kids about little stuff in the face of evidence to the contrary.
If you are crying and overpowered by this stuff, you need support for parenting challenging kids. There are techniques you can learn to help you stay calm and deal with this without buying into it. When you get so worked up about a kid's stories, you're more worried about some outside pressures. That's more common when there are custody or divorce issues. Please get some family counseling help for you and also your daughter so you have some help - every single parent needs an ally.