My suggestion:
Day 1
Arrive at Euston, drop bags off at hotel. Presumably you're arriving earlier and won't be able to check in, but most places will let you put any bags in luggage staircase.
From Euston station, take the Victoria line south to Victoria station. From there, ten minutes walk to Buckingham Palace.
From there, 15 minutes walk to Westminster. You'll go past Westminster Abbey, then Houses of Parliament with Big Ben. Here you are at the end of Westminster Bridge so you have a river view and are opposite the big wheel.
From there, 5 minutes walk around the corner to Downing St. You don't see a lot here, you can stand at the end of the street behind a gate and look up towards the famous door.
From here, 10 minutes walk up to Trafalgar Square with Nelson's Column.
From here, 10 minutes walk to Covent Garden. Either spend the evening here, plenty of food options, or snack here and get cheap musical tickets.
Day 2
From your hotel, walk to either Euston Square station or to Kings Cross station - both are next to Euston but opposite directions so depends where your hotel is nearest.
From either of them, take the Circle line to Tower Hill. Visit the Tower of London, it's great! It's London's top tourist site!
Here you are right on the river so you have the river view, The Shard is almost opposite you and Tower Bridge is right next to you. I'm 99% sure it's Tower Bridge you want to see with its fancy design and bright blue colour, not London Bridge which is plain dull concrete 
There is a website you can google to check what times the bridge is lifting up, if it's due when you are there it's worth watching.
So personally I wouldn't bother with a boat trip, you will have seen the river from Westminster and from here. But if you really want to you can take a boat trip from here next to the Tower.
Otherwise, from Tower Hill take the District or Circle line to Embankment, change lines to Bakerloo line and go to Piccadilly Circus.
Here you can see the well-known view of the big screens - not really that exciting but you're going past it anyway... Walk 5 minutes up Regent St to Hamleys.
From here, you can go back to Piccadilly Circus and take Piccadilly line to Knightsbridge, walk 5 minutes to Harrods. Personally I think it's a bit overrated, overpriced, but I know tourists do like to see it.
From here, you are probably done - depending what time your train home is.
Extras: you could add in the big parks - St James park is lovely and is between Buckingham Palace and Westminster. Hyde Park also lovely and is next to you from Harrods or a short walk from Piccadilly.
Art galleries in Trafalgar Square, and/or the big museums next to Knightsbridge (Natural History museum, Science museum).
If you have a contactless card you can use that for travel, no need to buy a separate ticket. You touch in and out when travelling underground, or just once when you get on a bus. Your 6 yr old will be free, not sure about 12 yr old. Look up the TFL website and check it.
I've including a lot of walking routes because it's honestly better, you'd be surprised how easy it is to walk between places and you see things on the way. Don't be tempted to spend half your time underground!