Several options:


Safest route:
1) When there are less than 14 days before the trip, get an emergency appointment at a passport center. Or line up and wait. They should be able to do everything same day.

and/or

2) Contact Swedish Embassy/consulate near you. Explain the circumstances and also include the fact that Covid disruptions have made it difficult impossible to get their passports done in time, explaining that you will still leave far before the passports expire. IF they say it is ok, then that letter/e-mail should be enough for the airline, and will def be good enough for Swedish passport control.

If you are brave, and know what you are doing.

3) Go to a notary and make a notarized signed statement (for the airline) saying that you do know that your kid's passports have less than 90 days of validity BUT you all still want to fly and you will not seek compensation and will hold the airline NOT RESPONSIBLE for any costs should you be denied entry into Sweden. Ultimately this is all airlines care about, which is ultimately the cost of returning you and a possible fine. In my experience Swedish passport control will care less, especially as Swedes can travel to the US up until the day their passports expire I believe. Again, this is the brave route that I only follow when I am very familiar with a country and their "rules" on the ground, otherwise you are opening yourself up to potential serious costs.