I always play with my little one on PS3.
We use the split screen. My daughter is player 1 and I'm player 2.
When we start MC you will be a single player. I can switch on as player 2 by clicking the start button.
But how can I play single mode? Even if it's not there, will your Player 1 be loaded first?
Well yes it works if you switch on the first controller your child is playing on and start registering this controller for the user of the account on the Minecraft, then switch on the second one and then you should tell which account your second controller should be assigned to now there are two options.
You go in case 2. Don't go out into the world and build in your daughter so she doesn't die.
On the other hand, it went as far as I can remember when there was no server on the console that if you enter Player 2 in Minecraft you have the same world, but it may not work anymore.
just put the inventory into a box after each play and everyone takes their stuff when someone is playing
I hope I could help on the other hand there are also servers which you can buy for cheap money (only 2 slots) because you are two. I myself have one with 10 slots that cost me 15 euro for 90 days a year maybe 35 because you pay in advance and not monthly.