What's the travel date? Perhaps the train is almost sold out.

Otherwise simply book for 3. The 2 yo doesn't need a ticket/reservation.

Travel date will be later in September or beginning october. Actually, trains for these dates are not bookable yet? So I searched for dates in the nearer future, e.g. 8th of september. Is there a way I could find out the prices without entering my Interrail number (I have not activated yet..)?
And about the 2 year old: Yes, she does not need ticket/reservation, but I am still wondering why the system does not know it (I entered her age). So I thought about rules e. g. for fire security, ...

You already have pass numbers: they are in your confirmation email. No need to activate the pass to book reservations, never do that.

I suggest using the VY app or website for the most reliable info.

2 year old: she would need a reservation to get a bed. Otherwise they don't care.

Side note: there are multiple issues with that line at the moment. 3 derailments, lack of maintenance, congestion due to the many many ore trains, etc.

Most trains are replaced by buses from Boden or Kiruna or you have to take another night train and change in Boden (7pm arrival in Narvik). Basically don't expect to get a direct train and be flexible. 1-2h delays are frequent.

My friend had to change plsns and spend a night extra in Narvik because of that (travelling in early September).

Thank you! Yes I heard about the problems, but I am still optimistic that there will be no more derailment ;-)
How is it in the moment? When I book a night train to Narvik only a few days in advance, will it be like on the vy-website or is it already “silently” planned to be replaced by a bus I only get to know when arriving?
I would also be flexible, but I am not sure, if the accommodation options in Narvik / Lofoten will be in the end of september? Travelling with my family is not so easy to sleep just anywhere like when travelling alone ;-)

What about the route via Ostersund from Sweden to Norway as an alternative? Is it recommendable?

The timetable should follow what's on the VY website.

By flexible I rather meant: don't expect to reach the Lofoten on the same day. Instead spend the first night in Narvik. You'll make it to Narvik at some point but until the timetable is released you don't know if it'll be at 2pm, 4pm, 6pm,… -> too late for the bus.

Accommodation is expensive and limited in that area but fortunately busy season will be over. I'd still book soon.

Östersund - Storlien - Trondheim could be doable yes. Note that the Norwegian bit is replaced by buses until further notice.

The connections on the Swedish side aren't particularly good either. There's a convenient Snälltåget night train though.