10 days to 2 weeks would be two or three cities, max. For a younger person with 2 weeks, 4 cities would be OK, but less would still be preferred.
Starting in London makes a lot of sense - lots of flights from the US and no language barrier. So I would start there, for 5 nights or more. Remember the day you arrive will need to be pretty low-key. Jet lag will be a strong possibility so take it easy that day. The rest of your time there could be spent exploring London, perhaps with a day trip. Options could be Oxford, Cambridge, Bath, Stonehenge or others.
After London you can do more England . Or leave the British Isles and head on to mainland Europe. That would be my suggestion. Take the Eurostar train. Paris would be the easiest, and most obvious. Other logical choices would be Belgium (Brussels is fine, but you'd want to head to Bruges or Ghent more) or Amsterdam.
So half your time in London (with day trip) and half in Paris (with day trip) would be logical, easy to get between, have only 2 different hotels, and offer a lot to do in a week in each. My suggestion.
However, if you or your mom wants to go somewhere specific, London will have plenty of direct, inexpensive flights to most cities in Europe. Rome, Florence, or Venice are often of top interest to first-time visitors, for example. So half in London, then fly to Florence for the second half.