The answer is no.
Too little time, too many in the group.
Drop the HoHo bus. Big waste of time as London traffic is abysmal.
Day 1: Up early, tube (Circle Line ) from Bayswater to Tower Hill (about 30 minutes but no train change). Walk across the road from Tower Hill Station to get in line to buy tickets for the Tower of London.
Tour the Tower, then walk over Tower Bridge. Follow the river path then over to Borough Market for lunch.
After lunch take the Jubilee Line from London Bridge to Westminster. Exit and take your Thames River Cruise. Then back to your accommodation to rest, freshen up and head out for dinner and then Hamilton. The closest underground station to Hamilton is Victoria.
Day 2.
Eat breakfast then tube back to Westminster. Exit and fight thru the congestion on Westminster Bridge over to the Eye. Doubt you’ll get immediate tickets to ride right then so you’ll need to be flexible. Get your timed tickets and then consider:
(1.) walking back over the bridge to Birdcage Walk which takes you through St James park up to Buckingham Palace. If the flag is up Her Majesty is in residence.
Pretty certain the younger members of the 10 will like seeing all the ducks, geese and waterfowl in St James Park. From the Palace walk past the Victoria Memorial and then down The Mall towards Trafalgar Square. At the end of the park turn right on Horse Guards Road and see if the Horse Guards are out
On the parade grounds. If not walk to Trafalgar Square and from there into Covent Garden. Punjab is a fabulous Indian restaurant there. Can’t miss it. Painted purple.
After lunch it’s about a 25 minute walk from Punjab back to the London Eye.
What you do after riding the London Eye is up to you.