Lauterbrunnen and Zermatt in 7 days end Sept/Oct

Hi ! I am new to this forum . Thanks in advance for your help . I am planning a trip to Switzerland onwards from North Italy ( Milan ) with my husband and 10 year old son. . I will be in Turin for work from 16-20 September. We have 2 weeks from there to travel and would like to visit Milan , lake Como area and Lauterbrunnen area .I have been to lucerne/ Jungfrau / lake Geneva before . This time we would like visit the Oberland area and questioning if we should also visit Zermatt and maybe try to fit in the Bernina express.We are nature lovers , love to walk / hike , like to have some quiet time and slow pace during our holiday but would like to not be completely away from activity/ people . Access to varied food options and some fun stuff for my 10 year old other than hiking would be nice ( he is well travelled and can easily cope with long hours of activity) .Budget is not a big concern but we like to spend it on better accommodation and food and would like to avoid constant packing unpacking .

I have done a fair bit of research and looked at Google maps and SBB train timetables and the forum questions here but still unsure about the best way to plan this . I I would appreciate your help please with the following:

1) How many nights in Lauterbrunnen area ? We have approximately 7 days for Switzerland. Thinking of 5 nights here. Wengen or Lauterbrunnen as base ? Wengen looks great but I not sure if it would be the best base for day trips and food .

2) We were initially planning to visit Zermatt ( 2 nights) but it’s kind of hard to get to with train changes etc , weather dependent , some say it’s very touristy and busy . I am questioning going to Zermatt now . Should I ? We will be doing a fair bit of hiking around Lauterbrunnen, would Zermatt be a repetition of similar scenery ?

3) Bernina express ? It seems to be on a different route . It it worth doing a few destinations along this route . I thought of this over GEX as it would be a different area of Switzerland. If it’s worth doing I will figure out how to fit it in .

4) Last week of September or 1st week of October? At the moment I am thinking finishing Milan / lake Como in last week of September as I will be in Turin then Milan to Zermatt or Lauterbrunnen 1st week of October , fly out of Bern . However if last week of September is better in terms of weather and closures , we could do that also , I guess .

This is a long post so thank you for your patience. ANY help is appreciated please .