Urgent help!!!!!

You cannot have an unlocked iPhone 3G that is not jailbroken. You must jailbreak and keep jailbroken an unlocked iPhone 3G.

 

All of this is moot if the baseband has been upgraded to a point where it can't be unlocked. What is the baseband version?

You can hide the Cydia icon I suppose, it will behave like a regular iPhone when its plugged into iTunes, she will never know.

 

1. Since you have 3G, it is untethered. Don't worry about tethered jailbreak.
2. You will have no issue with Itunes if you keep 4.2.1 because that the latest firmware for 4.2.1. If you unlock it and bring it down to 3.1.3 and give it to your mom. When she plug it into Itunes, Itunes sees it has an older firmware and ask for upgrade, she might hit update and restore, then you are facing an issue because in order for you to unlock it, you need an ipad baseband and once Ipad baseband on it, you can't restore to official firmware.
3. There is way to delete/hide Cydia from screen.

Use redsn0w 0.9.6rc16 to jailbreak, install ipad baseband on your 4.2.1 iphone, then if you want to downgrade, you can do so by downgrade it to 3.1.3 (no need shsh blobs to downgrade).

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Use redsn0w 0.9.6rc16 to hactivate it and it will bring your phone to home screen.

 

Redsn0w is jailbreak tool and not unlock tool. Use redsn0w to hactivate your phone and bring it to home screen. Once you are there, you can go to Setting, general, about and look at modem firmware and see what you have. I think you do have 05.14 or 05.15 baseband which can be unlocked by ultrasn0w. So, you probably need to put the ipad baseband 06.15.

Iclarified.com has all tutorials to jailbreak your phone.