Should I keep cat with fleas?

Recently I was gifted two cats after asking my parents for one for years. Originally we asked a breeder for one but they dropped off two saying the make them stay overnight and then send the one we don't want in the morning. Of course that was a trick and we realized that the cats were bonded and we couldn't separate them and had to keep both. Everything was okay up until yesterday when I realized that the kittens had fleas. After researching I am a bit terrified of flea infestations and realized my family might not be financially equipped to handling the medical fees or two cats. Flea treatment options that may not work plus constant vacuuming and cleaning to get rid of fleas are costly. I fear that if one of the kittens come down with something serious in the future we most likely may not be able to pay for treatment. I have informed my parents of this and that I think they need to be re-homed to someone who can afford their associated costs but my mother insists on trying advantage 2 and light cleaning in attempt to getting rid of the fleas. I am sure this won't work because of how full our small house is and the fact that she really isn't taking this seriously. I am very scared of a flea infestation and don't know what to do. Am I overthinking?