Oh, I'm so sorry you're struggling with this. Yes, it does get easier, but no one can say when.
My advice: Is there anyway your family can swing a post partum doula for a few days a week? (I work as a Lactation Consultant and a post partum doula and I know the agency I work for is a godsend for a lot of struggling parents.) The nice thing about a hired post partum doula is that she takes care of YOU, and you can direct her to do what needs to be done, so you can be with your kids. If you want her to take the baby and rock her for a while, she'll do that, if you want her to take the toddler to the park or just play or color with her, she'll do that. If you need her to make lunch and dinner so your family gets a healthy meal, she'll do that. She can throw in some laundry for you, fold it and even do your dishes if you need that service. And unlike family members, she's not going to try to change the way you parent, try to "get" the baby from you, bug you to "please let me give the baby a bottle" (unless that's what you want her to do) or anything else that happens when some family members come out to "help."
You can Goggle "doula services" or "baby nurses" or call a local Lactation Consultant and see if she knows of a service, or talk to someone in a local LLL group to see if someone knows of a doula service in your area. Do make sure the doulas are trained, insured and have had background checks.
It can be really challenging to settle in with a new baby, especially with a toddler who needs a lot of time, too. (And who ever heard of a toddler who didn't need a lot of Mama's time?) I also found that nursing in bed or in a Lay Z Boy with the toddler on one side and a book in one hand was really helpful. My first two were 26 months apart, and I had a C Section and was pretty much on my own after my DH took only a few days off of work (he went back to work the day after we came home with my pre term 3rd!) I pretty much corralled the toddler and myself into one room for the duration of the day, with snacks and drinks, as I couldn't get up and chase her after major abdominal surgery. Yes, I used the VCR (my kids are a bit older) and I saw it as a gift from Above! We watched more TV that summer (I had also been on bedrest for almost 6 months before the birth of my 2nd) but at least we were all together.
My foster sister did come a few times, did my dishes, did some laundry for me, played with my toddler (she is the oldest child's Godmother) and held the baby when I absolutely needed to lie down and Baby wasn't down with that. She was still at University, so she could only come when she didn't have classes or wasn't working, so it was sparse, but boy, did I look forward to those days when she could come even for a few hours!
If I had known post partum doulas existed then, I would have moved heaven and earth to get us one. If that is out of your financial reach (although I would have taken out a loan to get one with I had my second IF I had known they existed, and could have found one) then perhaps you can find a teen mother's helper. I know our LLL group had some home schooled teen girls who would sometimes help out with new moms, or even a neighborhood girl who can come and maybe take your toddler for a walk when she gets home from school? A teen isn't going to get "all up in your business" about baby care, so for many it's a safer choice than a family member. Unless you have a niece or young cousin who has some time for you.
It will get better, Mama. You're doing the best you can, maybe with a little help and a tincture of time, things will improve soon.