We went to Buckingham Palace yesterday - DH, 11yo DD, DM (aged 76) and me. We pre-booked the whole day experience, makes no difference still involves vast amounts of queuing to get passed security at each site.
Do go and see the Royal Mews, plenty of child appeal. DM had face at smell. Who know horses smell like horses 
bloody hell, Mum.
There are cafes across the road from the Palace. Bear in mind they won't sell just a [tea] to sit inside with at lunchtime understandably. This caused a row with DH and I. I insisted we go back to Starbucks at Victoria --for a decent cup, WIBU 
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The only timed part of the day was entry to the Queen's Gallery. The exhibition is the Georgians. Had I known that I wouldn't have bothered. It was very boring.
You are advised to visit the State Rooms last. This is because seeing Buck House is like a trip to Ikea. Once you're in the only way out is the exit. The rooms are fab and The Royal Toys Exhibition is what we really went for and is very good. Bear in mine the only toilets at the actual Palace are at the end, so go before you go in. The café in the garden is also at the end when you are gasping. The prices in the cafes are very expensive and the tea is dreadful.
Exit from Buck House is through the gardens (beautiful) on to Grosvenor St. Do get a bus back to Victoria, your feet will be killing by this time.
We didn't use the tube because of DM who doesn't do tubes. We took the 11 bus to Liverpool St. All agree this was best part of the day. the no.11 goes past Westminster Abbey, Houses of Parliament, Trafalgar Square, St Pauls Cathedral may not have got them all in right order.
HTH