OK, you've got a few different ways to handle this.
First, if you install a bypass module and remote starter in the regular, usual way, it will allow the remote starter to start the engine, but will NOT allow a non-chip hardware-store key to start the engine. Otherwise, anyone would be able to steal the car with a screwdriver and some know-how.
The above information applies regardless of whether it's a key-in-box style bypass, or a no-key-required kind.
That being said, you have a few options here that can keep your cost down somewhat, especially depending on how concerned you are about keeping the car secure.
1: Install a remote starter, and ALWAYS use the remote starter, every time you drive. You can make some $2 keys at Wal Mart or wherever. You only need the expensive chipped key during starting with the key.......you can remote-start and then take over and drive away with the non-chipped key.
Downside to this is that the aftermarket remote control is not a military-grade product. It'll work most of the time. And then eventually the remote's battery will die, or you'll get it wet at the beach or something.....and now you're stuck at the beach, waiting for a tow truck. Not good.
2: You could, as in #1 above, make some non-chipped keys, perform a remote starter installation.......but have the car's keysense wire also turn on the bypass module under the dash. Now, when you insert the key, the bypass module turns on, and then the car can start with the key. This is not hard to do.
However, you'll be basically permanently disabling your car's anti theft system. There are legal issues to this, as well as maybe some repercussions from your insurance company if the car is stolen and they find out what you did. So if you do that, do it at your own risk.
3: The Jeep dealer charging you $225 is because the remote-head key is very expensive. You don't need a remote-head key. You could get a regular, plain gray Chrysler Sentry Key, and install an aftermarket remote starter with its own lock/unlock buttons.
The key is still probably around $30-50 list price, plus anywhere from 1/2 hour to 1 hour dealer labor for programming. But that's still less than $225.
Also be sure to call a few locksmiths. They may have a better price, and/or many of them are mobile and come to you. Even if the price is the same, the convenience may be worth it.
4: Want to do something really super simple? Does the car only have one main driver? Do it this way:
---Install a remote starter in the usual way, with some kind of no-key-required bypass. All your daughter really needs is a 1-button because of the remote-head key she already has.....but you could do remote start/keyless if you want.
---Go down to the hardware store and make a non-chipped key. Or a two of them maybe.
---Hang one of the aftermarket remotes on the keychain with your existing good Jeep key. This is what your daughter will use for everyday driving.
---Put a non-chipped key in your daughter's handbag, in case she locks her keys inside the car at the gas station. This key won't start the engine, but it will get her into the car, at least.
---Put your second remote-starter remote with another non-chipped key, and leave it in the house. This is your emergency, back-up method of driving the car.
You can remote-start the engine, use the key to unlock the door manually, insert it in the ignition and drive away.
Daughter is late for work and can't find her good keys? Daughter is away on vacation, her car is blocking your car in the driveway and you have to move it? Et cetera and so forth.
Basically, use this remote/key setup for occasional, emergency use. Just don't go driving the car to Florida or something and get the remote wet at Disney, and you'll be fine.