I wish to commend you on your desire to introduce your kids to a musical instrument at a young age. If they succeed in developing a desire and ability to play an instrument, it will provide a lifetime of enjoyment as well as help with the mental development of timing, coordination, counting, and so much more.
One of the first songs I teach beginners to play on guitar in standard tuning is the nursery rhyme song Frère Jacque > Frere Jacques Wikipedia.
It's a one chord song which works like magic if your child (or another vocalist) can sing along. It can be played in the key of G in standard tuning by playing the simplest form of a G chord - fretting the high e string on the 3rd fret and strumming the top four (thinnest) strings. XX0003
Use a simple two strums per measure strum pattern all downstrokes. This will get the budding guitarist to start developing simultaneous and coordinated use of both right and left hand. It will also introduce the concept of timing and rhythm with the simplest of strum patterns.
If it proves too challenging to fret and strum simultaneously or your future rock star has trouble hitting the top four strings without hitting others, you can tune the guitar to open G and let them play all six strings. In open G or any open tuning, you can get away with strumming anywhere from all six strings to just the top 3 and anywhere in between and it will sound like the chord corresponding to the open tuning (Open G, Open E, Open D, Open whatever).
Eventually you want to get the student using the fretting hand in coordination with the strumming hand. But even in an open tuning the student can develop some rhythm and work on steady, even, consistent strumming to the beat.
The strumming pattern using English lyrics is as follows (strum on accented words):
Are you sleeping ... Are you sleeping
Bro ther John ... Bro ther John
Morning Bells are Ringing ... Morning Bells are Ringing
Ding dang dong ... Ding dang dong
You can also sing Row Row Row your Boat as a one chord song using the same concept.
Row Row Row your boat ..... gently down the stream ..... etc.
If necessary you can simplify the strum pattern even more by making it one strum per measure before graduating to two. Just strum the chord on the first beat of each measure and let it ring until the first beat of the next measure.
Are you sleeping .... Are you sleeping
I find it much easier for a beginning student (especially a younger child) to play a chord than to attempt to get the syncopation and timing of the various whole, half and quarter and eighth notes - to play an actual melody. And even more advanced guitar students have a difficult time with the alternate picking involved in playing a melody. Isolating the right single string in the correct order without accidentally hitting an adjacent string is something that even I find challenging at times.
So starting with a simple chord in either open tuning - or the four string G major in standard tuning - will get any future musician up and running with an actual song faster than anything else I can think of. And until they can master the timing for such a simple strum pattern, there is no need to try to teach anything more advanced.
Have fun making music with your kids!