So Apple's walled-garden approach to the iphone has breached the boundaries of itunes and has expanded to encompass your home...

I'm sorry to hear that.
It sounds like your Mom is not tech savvy, so any up-front touting of Android's superiorities is going to be lost on her. Particularly because you just can't get passed the wall she has built about Android's shortcomings. So IMO, you best arguments are to simply have points that nullify her arguments. It's not her fault that she is misinformed, but you need to make it clear that she is misinformed if you want to stand a chance of convincing her. The objective is to get her to see Android and iPhone as being on an even field, by eliminating the negatives that she sees in Android.
No Facetime?
- Tango or Skype is compatible across both devices.
Viruses?
- iPhones are only safe while they are confined to itunes. If the device is jailbroken then all bets are off. So you're going to be at risk either way.
- Alternately, there are antiviruses for Android.
- Alternately, I believe Android viruses are normally distributed through questionable apps. Avoid the fart apps, pron apps, and the like, and you'll avoid the viruses.
Lack of Uniformity?
- That's true. If having a larger selection is a bad thing, then I guess the larger selection of Android hardware is second to iPhone in this area. However, that also means that the size of the itunes appstore makes it second to the Android appmarket.
Once you can get it through to her that her own assumptions about Android are false, and that the two devices sit evenly (as far as she will be concerned), then she will come around and ask you why you want to bother with Android if they generally the same thing (remember, the point is not to show her how much better Android is than iPhone, it is to show her that her concerns about Android are misplaced and that Android and iPhone are largely compatible for everything that concerns her).
When she asks why you would want to change if they are basically the same thing (remember, she's not tech savvy so basically the "same thing" is going to mean smart phones that are compatible with each other), reiterate that they are the same thing as far as general app compatibility is concerned. BUT... now insert your reasoning here.
At this point she will probably either accept that she was misinformed and that you have done your homework, or she will retreat back to the previous misinformation that was already corrected. Good luck!