>> I'm planning a baby moon trip with my husband in March ... - Day 1: Arrive to Zurich from London, take the train to Adelboden, check into The Cambodian (fell in love with this hotel! It's relatively very well priced as well)
You can get the train as far as Frutigen, and after that you continue for about half-an-hour on Bus 230 to the stop called "Adelboden, Post".
>> Day 3: Leave Adelboden towards Interlaken where we want to visit HarderKulm
Unfortunately the Harder Kulm funicular closes during the winter, and doesn't reopen until 14 April.
Instead, you could consider going up to Wengen for an hour or two, where you will get wonderful views of the Lauterbrunnen Valley and surrounding mountains if the weather is clear. I have attached a map showing how to get to the Wengen lookout, and a photo showing what you can see from there. You could leave your luggage in lockers at Interlaken Ost station.
>> and continue towards Lucerne where we'll stay for a night or two
The gondola to Titlis and all modes of transport to the Rigi will be operational in March.
The cogwheel train from Alpnachstad to Pilatus Kulm will not be operating, but you can go up and back via the cableway from Kriens.
The new funicular, from Schwyz to Stoos, will also be operating. It is the steepest in the world, with a gradient of 110%.
Boats on the Vierwaldstättersee (Lake Lucerne) will be operating to a winter timetable, which you can consult via the following link. Be sure to read the explanation of symbols.
The funicular and cable car to the Stanserhorn is closed for the winter and doesn't reopen until 14 April.
You can plan your trips using the Swiss Timetable: