Can I use find my iPhone to track my daughters phone if we each have different apple ids?
Only the main Apple ID on the device (the one that has iCloud backups available) is available to log in to Find my iPhone. Any secondary iCloud accounts added to the device can not be used to track the device.
If she doesn't mind that her Apple ID won't be the main one, then yes, you can set it up with your Apple ID as the main one and that will work fine.
Also, if she doesn't mind, you can log in with her Apple ID.
If not, you can use Find my Friends since this works across multiple Apple IDs.
The consolidated answer is: YES, you can use Find My iPhone to track someone else's iPhone, so long as you know the main Apple ID and password that is being used on that phone. To track the phone, install the Find My iPhone app from the App Store on your phone, then log into the app using the Apple ID and password being used on the other phone (i.e., your daughter's Apple ID).
If you don't mind your daughter knowing that you are tracking her location, then the Find My Friends app (also from Apple) is a better solution for tracking since it allows you to track multiple phones simultaneously without having to log into the their Apple IDs, and allows geofenced alerts (e.g. "alert me when my daughter leaves school"). One potential downside is that using Find My Friends will also share your location with your daughter (and anyone else you are tracking).
To directly answer your question, you may use Find My iPhone to track your daughter's iPhone using the Find My iPhone app that you can download from the app store - without any consequence to your own Apple ID that is in use on your device. All you need to do is sign into her Apple ID in the app, and it should show her device (as long as Find my iPhone is enabled on her device).
When using the Find my iPhone app, you can keep your Apple IDs completely autonomous, and all you need to know is her Apple ID.
Like @grgarside mentioned. Find My Friends would probably be a better option either way since you can set up geofence notifications, and such.
"Track" may not be the most accurate term. You can "locate" (or find) your daughter's iPhone, but only if she has the app and iCloud enabled. If she turns it off on her phone, then you will not be able to locate her phone (or her). The app does not "track" in terms of showing you where she as been, from location to location. In other words, she could have it on when she's home, turn it off and go to the mall with her friends, then turn it back on when she gets home and you will not know - other than the app will indicate an "old location" when it attempts to find her phone and the app/ iCloud are turned off.
Answer for ios 13+:
- On your daughter's phone, open the
Share My Location
- Select yourself to share her location.