Aside from Oxford Street and Regent Street, Carnaby Street looks amazing. Bond Street also looks lovely. The shop window displays in these streets are also lovely.
Liberty (near to Regent Street and Carnaby Street), is always beautiful, and Piccadilly always feels Christmassy to me, but mainly for the shop displays than the street decorations.
If your Mum and children could travel up before the rush hour starts, then that would make for a more comfortable experience. Perhaps they could go to a café in one of the backstreets upon arrival just until it gets a bit darker if necessary. I would advise walking to all of the destinations rather than taking the tube or buses (if your Mum is able), as the transport will be insane during rush hour (including entry and exit of stations, not just on the trains). You also get to see so much more too.
When walking between ‘light’ destinations, they could always walk in the far less busy backstreets - I’m a Londoner and always do this. Your Mum could plan a route beforehand to use the backstreets.
They could exit at Piccadilly Circus & have a little look at Piccadilly if they wanted, then walk along Regent Street for a while to look at the lights, then cross over to the Hamleys side of the street to access the backstreets to Carnaby Street. Walk up from there to Liberty, then out into Oxford Street (near Oxford Circus junction). They could cross the road (to be on the flagship Topshop side), then walk up Regent Street again for about 100 metres, then take the backstreets around the back of Oxford Street. They can then see the back of John Lewis etc, and your Mum can use this as a guide as to popping back out onto Oxford Street at particular locations to see lights and particular shop displays. Walking along the backstreets, they could also re-enter Oxford Street via St Christopher’s Place - this is another beautiful little area (walk straight through to Oxford Street). It leads out pretty much opposite to Bond Street tube station, and Bond Street itself is down the side road near to the station, so they could wander down there for a while for lovely lights.
Alternatively, would it be possible to travel up just as rush hour is winding down and spend a couple of hours there, before travelling home? Perhaps not on a Thursday though when late night shopping is on.