My sister-in-law was a single parent with twins.
Those of us who have never been in that situation often make assumptions about how hard it will be; those actually in the position tend to find practical ways to make it work.

To the OP - you'll need to buy a 2nd seat, but presumably that's no extra cost over what you would have spent if your husband had been able to make the trip.

From watching my sister-in-law manager with hers, I'd say that if you are able to handle trips to the mall and on public transport on your own with both twins then most likely this wouldn't be any greater difficulty.

I assume that you'll have somebody else to help you at the other end ? The main thing to think about is how you are going to get both twins and the car seat from the aircraft door (where they'll take your stroller) to your seats; you can reasonably expect some help from an FA with the car seat and carryon, but depending on where you're seated, you could end up carry both twins, your purse, etc over 100 feet when embarking and deplaning - you shouldn't rely on sombody else to carry one of the babies.