I haven't stayed at Fraser Residence Osaka before, but my research on the internet for my last trip did tell me that this hotel is a very good option.
It's very near Nankai Railway, making it very convenient to travel to and from the airport.
Not sure what airport express you mean but if you refer to Haruka of JR, it's not a good idea as there is no direct train from the Kansai Airport to Namba, and even JR Namba Station is rather far away from either Fraser or Swissotel.
With kids, probably the best choice is Fraser, but you have to check carefully for the suitable room / suite for your family. Ask your travel agent to confirm.