OP, my situation is actually very similar to yours, in the sense that ALL sick time, doctors visits, etc are fallen onto MY shoulders. But we have no choice.
In my husbands field of work, a utility truck/van is required to transport tools. We have NEVER had two family vehicles in the 11 years we’ve been together. Therefore, the only mode of transportation we have for the kids is my car. So when daycare calls and says one of them is sick and has to be picked up, it only makes sense for that someone to be me. I have actually gotten a “warning” at work (Albeit I found VERY unfair) that I had taken to much PT time for sick kids in the first quarter of the year. (um hello, as soon as one gets over something, the other one catches it, THANK YOU!) I was told that maybe my husband needs to start helping more. AS IF THAT WAS ANY OF MY EMPLOYERS BUSINESS HOW WE CARE FOR OUR CHILDREN. Its just not a feasible scenario. My husband would have to leave the job site, which is sometimes an hour in a half away from ME to come get my car, and then drive another 20 minutes to the daycare. By that time, almost 2 hours will have passed. Doesn’t make much sense does it?
Because of this scenario, my husband has NEVER met the kids doctor. (Something I razz him for occasionally) My point is, the scenario you describe might not seem so exhausting if you weren’t in the situation your in. (a completely useless partner who does NOTHING to help, not just carting kids around)
Very rarely can my husband stay home with the kids, because, in his line of work, he doesn’t get paid time off. Never has really. He did a couple times this winter (it was a hellish sick season) But there have been times he was actually working out of town, and I had to jump through hoops of FIRE to get to work because I had no time left. Did my employer appreciate that? OH HELL NO. I have a better support system then you do. (I feel awful about your lack of support) My mother, MIL, SIL, FIL, Aunt, have all pitched in at one time or another so I could go to work. Its miraculous, really. It takes a village, atleast in my life.
To answer your original question, I now, after 8 years of service, get 4 weeks vacation time. I earn 8 hour of PT time (Which is what I need to use when I get called away last minute) every 2 months. Whatever PT time I don’t use by the end of the year, I can roll over, but that rarely happens anymore. We get roughly 10 paid holidays, 2 of which are floating. I don’t have to worry about the daycare shutting down during school holidays because they never shut down. I save as much vacation time as I can for the summer months, when I pull them out of daycare to go to my MILs every day (She works at a school, so it saves us 3250 to pull them out for the summer) This makes more sense because if I took vacations while paying for them to go to daycare, I would still have to pay for the weeks their not there. AINT HAPPENING. BUT, I cant roll over vacation time, I have to use it by the end of the year. I currently, with all my scheduled days off, have 22 hours of vaca left to use before the end of the year. I am hoiping that, once sick season hits again, I will have those to use for days I have to take off for a sick child, and bank as much PT time as I can.
I guess the point im trying to make is I don’t think it would matter if your husband had tons of time to take, or no time ever. Your situation is exhausting because you are emotionally drained from dealing with EVERYTHING by yourself. Not just the sick time and doctors visits. I mean, if YOU were sick, would your husband drop your son off for you so you could stay home and sleep?