I presume, though you don't specifically address it, that you are eligible for FMLA. Note that even if you qualify one given 12-month period, after that is up, you'd need to work almost 33 hours a week on average, every single week, to keep qualifying for FMLA. (That's because you have to work at least 1,250 hours in a 12-month period to qualify. If you qualify during one 12-month period and use FMLA, you'll still have to have worked 1,250 hours during that year to qualify for 12 more weeks in the new 12-month period. If you use up your 12 weeks' worth of time under FMLA, accounting for those 12 weeks leaves you with 40 work weeks within which to work those 1,250 hours. If there are any days your store is closed or you aren't scheduled to work or miss work for OTHER reasons than having to do with FMLA (including personal days) (let's say a very conservative two weeks a year), that narrows the number of work weeks within which you have to work the 1,250 hours a year down to 38. Twelve hundred fifty divided by 38 = 32.8947 hours a week.
"I am at most times unable to talk to my HR person because of the misinformation I am given by her."
If this is just a local HR person and there's a main dept. elsewhere, I'd contact them.
"With my diabetic son if he gets sick and throws up and is unable to hold down any food the possibility of him going into a seizure due to hypoglycemia increases greatly."
Not clear whether you are referring to an overall issue with colds and viruses that aren't a "serious health condition" causing problems that may or may not affect his blood sugar, but I trust you've also considered that the hypoglycemia might be a side effect of certain meds he's taking.
"Therefore I need to stay home and take care and monitor him frequently."
I gather missing out on earnings isn't an issue, but all I can tell you is to press the FMLA issue with a higher-up and, if you cannot resolve it and believe you qualify, then you file a complaint with the federal DOL (and/or pay a local attorney to send the employer a nasty note about FMLA).