Op I think what I realised when I became a lone parent after previously having an involved husband (no other parent involved at all now) is that the systems you put in place in your home are everything. You and your husband need to sit down and look at what your current systems are, who is responsible for what, and make a clear plan of when you each get down time. What jobs can be outsourced eg. Shopping online for delivery, robot vacuum/mower etc.
Your sister is completely irrelevant to your issues really - you are focusing on her because she's there and you're looking at her world with rose tinted glasses on. Your parents are essentially holding the place of a spouse in her world. You have another person who you can lean on when things are hard or run questions by etc. Your sister maybe doesn't have that with her ex. I also personally wouldn't want to be without my kid half the week and would also be trying to keep myself busy and occupied during that time even though on the outside it looks like 'fun down time'. It's certainly not something id aim for. If you want down time which is what your post is really screaming for, then you need to sit down with your dh and plan it.
You have chosen to stay at home with your kids which is a temporary arrangement which your husbands job is well enough paid to enable. Your sisters situation is probably permanent. When you feel the time is right you will then have the option of returning to work, meaning more income, more social time, more balance with your dh maybe. Your sister has had no choice but to work and the adjustment of her hours is neither here nor there. You say she has opportunity to socialise while working - that's not socialising it's networking and it's still work.
If you are missing feeling connected to other people then you need to look at who else is free during the day to create your networks. So local mums and tots groups or baby classes and make a conscious effort to make conversation. If your sister lost her job she'd be utterly fucked so you are in a place of real security in that you could both work if needed. How you plan your time otherwise is actually up to you so maybe you need to think more outside the box with how your spending your days.
What you're doing during the day is essentially 'work' you'd be outsourcing it to nursery if you didn't do it so when your dh comes home at the end of the day/ weekend he needs to be completely 50/50 with you on tasks.
You say it's harder for him to give you child free time with two- if God forbid you died tomorrow what exactly would he do? There are plenty of men and women out there lone parenting with two kids the same age as yours so unless there's a drip feed around illness or disability coming there really is no reason why your dh can't manage alone with your two kids for a few hours to let you get out of the house.
You say your dsis often works into the evening and works from home - working from home with a child that age is a nightmare. It's not childcare it's the same as being at work. Working into evenings as a single parent is also not easy, I've just changed job because I couldn't get childcare for evenings after nursery closes. I also hate that I get so little actual time with ds. I see him for about 3 hrs a day awake time which mainly involves getting him ready, driving to/ from nursery, doing dinner and bedtime routine. We get little quality time until the weekend and your sister is getting half of that. She's probably using her hours creatively to give her time with her child and using GP childcare to keep her job secure.
I'm not saying that to minimise the things that are hard for you, but to point out that there is a grass is always greener mentality that isn't going to serve you if you keep looking at what she is doing instead of looking at what your husband isn't.
That's why your parents aren't taking on extra work. They know it's your husbands work to step up to and they (rightly) don't want to give him an easy out. Your sister doesn't have a husband available to do that on certain days which is why they are filling that gap.
If what your husband can do is not enough then maybe you look at settling your youngest into a nursery for a morning or two a week or one day a week to give you some downtime.