No, she cant threaten to leave her husband as it would be an empty threat, she has children so this is not realistic and also its more likely to escalate the situation into a massive row.
I would do some decluttering now and whatever rearranging you need to do to accomodate them. As you have children your house might be like mine with more toys than you really need! Identify the space they are going to need and clear it without harrassing your partner, then show him the space.
Also are you planning to bring a wood hutch inside? My husband would be less thrilled about that but does not mind a correx or a plastic bottomed cage.
Also regarding the mess, consider fleece rather than messy beddings. Always open a hay bag outside (or if you are in a flat then open it inside the cage). Use a hay bag, tray or hay sock rather than a rack. And always keep a dustpan and brush next to the cage.
Can you tell I have had similar issues?!
Good luck.