She is probably just going through a developmental stage where she is so close to being mobile and moving around on her own. I would have the same trouble at nappy changes as you with the kicking and wriggling around. I would give them something to hold onto to distract them from moving for a bit while I changed them.

As for the sleeping, have your tried different bedtime routines, so she starts to learn when it is sleep time and not playtime? Is her room darkened for her at all? I found that by closing the blinds a bit that they would settle better than if it was light. I'm not sure about the Brauers as I haven't used it myself, but I know a few others on here swear by it.