Hardly any hotels within central London have car parks. The only ones that do are the super-luxury hotels, where you still have to pay mega-bucks to park there. Even in outer London it's unusual for the cheaper hotels to have car parks (or, if they do, they'll only accommodate half a dozen cars for a hotel with 30 rooms). It makes far, far more sense to take the train and then to use the Tube to get around London. (Booking 'Advance' tickets on the trains can get you some really good bargains. Post again, telling us the age of your kids and which station you'll be travelling from if you need help finding them).
To get around London, you'll either need a contactless debit card or an Oyster Card. (You can't use cash on the buses and paying cash for Tube tickets works out mega-expensive). Information here:
https://contactless.tfl.gov.uk/?intcmp=29807
Children under 11 travel free on buses and trains in London. Those 11 to 15 go free on buses and pay half-fare on the Tube. Information here:
https://tfl.gov.uk/fares-and-payments/travel-for-under-18s/travelling-with-children?intcmp=25255
Most hotels right in the central area are very, very expensive (typically charging several hundred pounds per person, per night). However if you book early you can find reasonable prices at some of the budget chains (such as Travelodge) which have a few hotels not too far from the centre. There are also loads of cheap hotels around the edges of the centre, in areas such as Kings Cross, Paddington, Bayswater, Bloomsbury and Earls Court. (There are also plenty a little further out at Stratford but it's still only a few minutes on the Tube into central London). This is an excellent website for finding cheap hotels in London:
http://www.hostelworld.com/
(Don't be put off by the word 'hostel' in that URL. There are loads of hotels and B&Bs listed there as well. Simply use the search filters to restrict your results to the type of accommodation which you're seeking. Take care to check the locations of the hotels and, of course, study the reviews carefully!).
There is no such thing as
the boat trip. There are loads of different operators running them. Apart from the really expensive ones (where, for example, you get dinner and a cabaret thrown in) you don't need to book; you can simply turn up at any of the piers that they run from. The 'proper' tours (with an official commentary) can be pricey; it's cheaper to use the commuter river bus services (where the crew often provide a commentary anyway and then drop big hints about leaving a tip!). Information here:
https://tfl.gov.uk/modes/river/
You hardly need to seek out the open-top bus tours. The city centre is full of people trying to sell you tickets for them! They're very expensive though, so you might prefer just to explore the city under your own steam anyway. Information here:
https://www.theoriginaltour.com/
here:
https://www.goldentours.com/london-hop-on-hop-off-open-top-bus
and here:
http://eng.bigbustours.com/london/home.html
The hop-on/hop-off bus tours can get you to Buckingham Palace. For other bus routes that pass nearby, see here. (Look in the bottom left-hand corner of the map):
http://24.media.tumblr.com/tumblr_lz440dRKRW1r54c4oo1_1280.jpg
The nearest Tube stations are St James's Park and Green Park.
However the station you should really be heading for with kids is South Kensington. The museums there are all free (apart from certain special exhibitions or attractions). The Science Museum is a kids' paradise, with loads of interactive stuff. The Natural History museum has got a moving dinosaur. Even the somewhat stuffier Victoria and Albert Museum has things to interest kids if you seek them out.