Passenger list information (in conjunction with the information from the emigration records) reveals that Hedda and the children departed Sweden on a ship named the Romeo, leaving from Goteborg, Sweden for Hull, England on 27 Feb 1891). This only would have got them to England, as the Romeo’s route was from Scandinavia to Hull, and to find where they landed in the US I will have to do more work.
Information on the Romeo. The photo above is from the same source. This site also is useful for providing some context on why people left Sweden for the US and also — why I’m posting it here — includes a map of common travel routes from Sweden to the UK, including the popular Goteborg to Hull route that Hedda (and perhaps August before her) took. Together, these two sites provide a great deal of information on the conditions and logistics of the trip from Goteborg to Hull and then Hull to the port (often Liverpool) where the Scandinavian immigrant would typically have left for the trip to the US.
Given how common his name was, I have not yet been able to identify August on a passenger list out of Sweden (although I have two that look like possibilities and am working on it) and also have not identified any of the family on a passenger list from the UK to the US.