From Tian'an Men in a straight line through the FC without deviation, left to the south entrance of Bei Hai Park and up the east side (but not around the top) to the north exit and across the road to the southern tip of the Shicha Hai (proper name for 'Back Lakes') and up the east bank of the Qian Hai ('Front Lake') to the southern tip of the Hou Hai ('Back Lake') would by itself be over 3.5km. The Hou Hai itself is around 1km long, with various turns into alleys with temples and shopping (and you've the Xi Hai ('West Lake') beyond that if you want to complete the set).

Assuming a deviation into Tian'an Men Square (itself about 0.75km long) that's all going to amount to a fairly long day on foot for children, even with a highly regrettable and overpriced made-for-tourists rickshaw ride to amuse them in the middle.

Why not just go with the flow and see what catches the children's imagination en route, hopping into a cab to complete the trip when tiredness strikes? There are, for instance, a fine exhibitions of clocks and automata of toys, and of jewellery within the Forbidden City itself, and the children may well find the labyrinth of smaller scale courtyards to either side of the main axis of the northern section more interesting than whizzing straight north past the main halls.

You might also consider other attractions of more interest to children to break up the multi-day onslaught of Ming architecture you're considering. The Planning Museum (just off the southeast corner of Tian'an Men) has a 3D digital movie of flying over Beijing, or there's an excellent little-visited railway museum in the northeast of the city with dozens of steam engines on which to clamber, for instance.

Peter N-H
China