Yes, you can install the same app on your wife's phone and entering the master seed to use the same wallet.
It's the same as both of you have the same access to write checks from a joint checking account.

Any transaction you make will also appear on her phone and vise versa.  They will both keep in sync.



If your phone is stollen, and you don't have any security setup (example finger print or code AND the app isn't setup with another code), then the person could take all your bitcoin from all the accounts.  It's worse than a bank card that you wrote the pin on the back.  Just might as well have lost a wallet with cash in it.  So, don't be dumb.... setup a pin code (not 1.2.3.4.5.6)

Basically, keep the master seed on paper in a safe deposit box.  If you lose your phone (knowing someone can't get into it), then simply get a new phone and reinstall the app and recover from your master seed.

Note: bitcoins on a phone should be considered a hot wallet.  Meaning, funds in it should be what you need for day to day dealings.  Not a storage device with all your coins.

'Hacking' a phone isn't as easy as simply typing in digits until you get the right one.  So, a lost phone is safe if you went through setting up security.  If you want real security, then get a trezor / keepkey to use in conjunction with your phone.  (You didn't mention, that I noticed, which phone you were using (iOS or Android).)

There is no need (for most people) to backup the private key.  The seed (12 words) is what is needed to backup all the private keys the app makes.  A private key for a single transaction changes for each additional transaction since mycelium moves from one address to the next.  Yes, there are rare instances you would need a private key or even a master private key, but those are for very specific reasons.