Is the child of the size it would use a bassinet? If so, try calling and having that assigned - don't think I've seen any reports post introduction of seating fees. https://www.flysas.com/en/travel-info/onboard/seats/ It also wasn't that hard to find on the website. I would doubt though that your partner would have their seat assigned.

I am not sure any airline guarantees a family is sat together above the minimum requirement of one adult per child under 11 (or whichever age the airline puts down, and can thus be sat apart). Whilst it is more convenient to be located together, it isn't a guarantee. European airlines have more or less gone for a seat payment model in business (AFKL, LH group, BA, etc...).