I am a mother and the one thing I always hear is "mommy I want to play a game on your phone!" My children are smart and very innovative, and it's hard to have to enable restrictions on the go just to let them use my phone. Wondering if there is a way to incorporate apps on the lock screen? Allowing maybe up to 4 apps to be allowed access with out the phone being unlocked. Solving the problem with having the phone open and your children deleting everything and going through everything. And also faster then going through settings and enabling and disabling features all the time. My children are 3 and 6 , iPad users as well. I love apple all around. I just wish there was a way for the iPhone to have a kids safe mode so they can enjoy the phone as well on long car rides or long waits in lines, without risk of your important apps or info being played around with. Just a curious mom right here! I'm sure I'm not the only mother who would find this option amazing!!
Kids safe mode!
Many (not all) of the options you are describing are available through the Restrictions section of the General section in the Settings app.
Others, such as suggestion to put select apps on the lockscreen, preventing children from being able to use the rest of the phone's OS, is not currently possible to implement because there are facets of the ecosystem that 3rd party developers have no control over.
You could also file a bug report or use the iOS feedback links to officially let Apple, Inc. know your concerns.
iOS user-centric queries are best put to the public support forums, I think, but feature requests are best submitted via the Report Bugs link below.
If you're asking how your app can participate on the lock screen for this, you may want to look to notifications, if at all.
Good luck in any case.
I would recommend using 'Guided Access'. This will allow you to triple click the home button to enable it. You are able to prevent your child from pressing the home button, changing the volume, and setting a time limit. They will need you to change apps for them though.
To setup and enable Guided Access, open up Settings -> General -> Accessibility -> Guided Access.
You'll need to enable it, then setup a passcode and turn on accessibility shortcut.
When you're ready to use it, open the app your child wants to use, triple press the home button. You can change what they can and cannot do under Options. Press Start before giving it to your child.