Getting around . children under 11 are free on tubes, buses,dlr, and no ID is needed. BUT since you have a 12 year old I suggest you look on the TFL website and decide what approach to take for them, maybe a child visitor Oyster card is the best bet. For adults use a contactless card ( I would use one each) and always tap in and out on the tube and dlr , and tap in on buses. This will cap your daily journey to the cheapest tariff, make sure you use the same card each time. On the underground look for the luggage gate at each station and use those so you get the littlest child through safely.
Tube lines are colour coded and stations have easy to use maps and are usually well signposted. Underground staff are invariably helpful, as are us natives, just stand on the right and don’t all cluster at the top and bottom of the escalators please :) Some lines are more straightforward than others ( side eye to the Northern line) but if you go wrong just get off , change platform and catch the next train in the right direction. Try to factor in at least one trip on the Elizabeth line to admire the engineering and the super fast trains. Those stations are DEEP!
Bus drivers are also helpful, but obviously are negotiating traffic etc so might not remember to give you a shout if you ask for a stop. Many buses have ticker tape signs to say where you are but not all.
For river trips the river bus is cheaper than the organised commentary boats. I would start somewhere like Embankment pier ( the Charing Cross side, ) and get a return ticket to Greenwich. This will take you on a great trip, past Tate Modern, the millennium bridge, Globe theatre, HMS Belfast, Tower of London, Tower Bridge and lots more places. If you wanted you could get off at Greenwich and walk up to the Observatory and the Maritime Museum . Then take another boat back. You will all have to pay, no free kids tickets.
One of my favourite walks is to start at Westminster tube station, you will see Big Ben looking wonderful, and the Houses of Parliament and Westminster Abbey, then walk up Whitehall, past Downing Street, past Horseguards ( check the times they change) up to Trafalgar Square. Then cut down the Mall to Buckingham Palace. On the way spot Nelsons ships on the lamp posts. Then if you have the energy walk through Hyde park to Kensington gardens.