No. You cannot get the strain H1N1 twice.
Swine flu, or H1N1 is nothing more than an influenza virus that used to be characteristic to pigs, hence the name swine flu, but it is still an influenza virus. This means that once you have caught the H1N1 flu, you cannot catch it again. Your body develops antibodies and memory cells that will remain in your body and kill any future infections before they can take root. This also falls in line if you received a vaccination shot with the H1N1 as part of the mix. It is a characteristic that is true for all influenza viruses. So if you caught the virus from your children, you don't have to worry about re-infecting them. On that same end though, if you happened to catch a different strain from them, you should still follow all the normal health safety procedures so that you don't run the risk of getting them sick again. The reason for this is viruses actually evolve and change, so there are potentially dozens of new strains each year to combat as a result of the previous year.
Do I Still Need a Flu Shot Each Year?
You are probably thinking 'well if I can't catch it twice, should I still vaccinate?' The short answer is, yes. The influenza virus changes every year and there are many variants that are out and about. The flu shot usually contains only the most virulent strains for that year, so it has the best chance of protecting you. Getting a flu shot each year helps to protect you for that year and for those strains in the future. The flu shot isn't a magic bullet that will guarantee you will never get the flu ever again, since you might come into contact with one of the more rare strains for that year. The CDC works hard on the vaccine to make sure it will do all it can for you, but they cannot pack everything in each year, so getting it every year gives you a larger blanket of protection.