Hi there and welcome to the forum!!
I do not play Dream Zoo, so I am unfamiliar with the multiple game feature it may or may not have. I do not think that it is possible to be able to play on your wife's iPad. What I recall is that the iPad is really intended to be a one person-user device. Yes, there are some things on the iPad that Can be shared, like books, etc-but really is intended for one and not multiple.
By chance, do you own an iPod touch? You could try to play your own game on that one if available.
Good luck and best wishes!!