Normally it takes 3-4 hours to watch Red Fort completely, so suggest you to carry snacks for your kids and do not forget to carry at least 2 bottles of water. For kids who can walk main attraction will be the big green garden as they can run and play there. You can find a good area to sit under the shed to have a quality family time.
Washroom are okay as they are on paid basis. You can find them behind the ticket counter. Do not forget to see Diwane khaas and Aam ....war museum too... If you find to see the light and sound show , go in evening because kids will not stay from morning till evening. Avoid weekend and Monday (it's closed).
You will see fountains without water , there is not much to see but kids will always feel good and excited to go out and a big garden will be treat for them. For you Meena bazar will be a grand treat inside the fort.
Needless to say avoid heat days and yes do not hire a guide , written explanations available everywhere.
India's one of the biggest monuments is definitely worth to watch.