General discussion is not really the best place to ask help with technical problems. Hearthfire has support sections for Xbox 360 and PC versions.
That said what platform are you playing on? If it is PC and you have any mods that alter where a spouse can live, you will need to get rid of the mod in order for Muiri to be able to move to the new home. The children move with your spouse, if you are not married you can talk with the children about where to move to.
That the dialogue said move somewhere else rather than move to your Falkreath home, and that Muiri moved somewhere she should not have and the children never moved with her, makes me think you are playing on the PC.