Er... Surely you could argue that this cage would take up nearly as much space and have considerably less?
Or maybe ask to get the hamster heaven/savic ruffy/ferplast mary e.t.c as an 80cm by 50cm cage that would be smaller than the two together but actually be big enough for Bubbles? And it'd look neater which might help convince her.
And sadly, a good improvement isn't as good as a big enough cage. Hadn't you got permission for a big cage before planning to order it? I thought your Dad had even agreed to help mesh the ZZ2?
Alternative good idea! Buy a big storage box and claim its for his carefresh/food e.t.c, make sure it has really tall sides and then convieniently let Bubbles live in it instead after a few days