Umbrellas and Goffins are fairly different though (in terms of certain behaviors)---Not saying that they aren't both cockatoos, but Umbrellas seem to be a bit more prone to problematic situations in general based on stats. A pair of Umbrellas (especially male and female) is probably not going to be as smoothly-operating as a group/flock of goffins...Just based on what I have heard/read (I don't own Goffins, but I do have an Umbrella, and it seems that Goffins may be slightly less uptight about things). A pair of anything is more likely to "pair off", if you catch my drift, and if the birds form a bond, they may drift from you in some cases (especially if one is less inclined towards a particular person).
Whatever the case, your wife can't assume that she will "have her own bird" because birds pick who they pick. Luckily for her, a cockatoo can pick more than one special someone because of their flock dynamics. Why not work to strengthen the bond she's got with your current bird? I do believe that relationships with birds (especially cockatoos) can be developed, even if they don't seem too fond of someone at first.
Yes, they tend to have a single person that they are obsessed with, but they can have multiple favorite people. In the wild, they pick a mate but then they continue to hang out as a big flock (unlike most parrots). This is one of the reasons that they are so socially needy. She should work with what she's got and try to get over the idea of having "her" bird. Even if you did get another (of any species) there is no promise that it would bond to her (and even if it did, bonds often change at puberty). When I first got my bird, it picked my boyfriend over me (he didn't even like her). We are good now, but that can and does happen and not all people end up with birds who like them. Yes, they say "let the bird pick you" but at the end of the day, there is a lot up in the air here.
If you get another bird, that would mean that you would need enough time to interact with both birds out of the cage at separate times (playing, socializing etc)----If they do not get along (or get along too well...), this may mean 2 totally separate times for all of their play/social needs. That's roughly 8 hours a day at 4 hours per bird (because Umbrellas need a lot of time). Even if kept separate, hormones and aggression and jealousy can still become an issue just from them being nearby and your new bird could be a screamer etc..You have to consider the fact that your current bird sounds very mellow and a new one in the mix could totally rock that boat. Typically a well-behaved bird will modify its behavior for the worse when around a less polite bird (and not the other way around).
It sounds like she wants to experience what she thinks you have with your current bird, but each bird has its own personality and in all honesty, you guys sound like you lucked out on round one. If she gets a different one for "her" and it doesn't meet her expectations/ behave like yours, it will have defeated her purposes for getting another bird and it will have complicated what was once a good thing.
A year is not all that long, so I would also consider the fact that your current bird could still change etc. My bird has been adjusting to new things and changing for years, even as an adult (she is 11). I didn't fully know her a year after adopting her (adult re-home), even though I thought I did. Much like a child, they learn and change over time---even as adults---since the one-year adoption mark, she has formed more healthy bonds with people etc. My bird put my little sister through the ringer for that first year (tested her, bit her, bullied her). My sister finally got over her fear and learned how to call Noodles' bluff/assert herself/read body language and now they are great friends! Noodles loves her to death, which wasn't the case for the first year.
I am just afraid that because your first experience has been so good, that you may end up in way over your head (mostly due to hormones and jealousy) but also due to potential behavioral issues and personality differences between birds.
I say this lovingly, but the stereotypical umbrella cockatoo is an obsessive, fickle, flying, two-year-old with a chainsaw, the volume of a jet engine (+ wings), and ADHD tendencies---that is the stereotype for a reason....If your current bird is nothing like that, he is in the minority.
I would not risk ruining a good thing---it sounds like you guys have a great situation and this plan to add a new member could upset the balance.