Greetings The_Pooka,
Thanks for using the Apple Support Communities.
I see that you would like to set up your iPhone SE so that text notifications on your favorites list come through, even when Do Not Disturb is enabled. It's important to make sure that you can receive the text message notifications that you want at any time, so I'll be happy to help.
It sounds like Emergency Bypass is what you need. In the Contacts app, find the card for one of your kids. Tap "Edit" at the top, then tap "Text Tone". On that screen, turn the "Emergency Bypass" switch on. You can do the same with calls by tapping "Ringtone" on the edit screen, if you like. You must do this for each contact for whom you want this feature enabled. Once you do that, you will receive their texts while your phone is in Do Not Disturb or silent mode.
Let me know if you have any questions.
Kind Regards.