OP, you can have exactly the same as her,
You could "dump" your child on your husband and go and do things, then the following weekend your husband can dump your child on you.
the thing about being a single parent, it is not she has him about an hour before school(really?) or a couple of hours after(really?)
It's when you are a single parent every job is done by you, rubbish out, tea cooked, stories read .......... every single thing,
you sit down at night on the sofa and have someone next to you to process the day with, another pair of eyes to notice and another pair of hands to lift, another mouth to nag,
When you are a single parent, everything is magnified, it not twice as big,it fifty times as big, or more.
And you don't have the luxury of trickle processing daily events, someone you can bouncy off, jump in and out of conversations with, it's incredibly stressful.
Your nephew is really lucky he has wonderful GPs who clearly want to help take pressure off their daughter.
You are not alone, hopefully your SiL will meet someone who adores her, she sounds like she deserves to be loved,
I would look around you count your blessing, and stop resenting someone who has a lot less than you,
how often does your nephew stay with you?
My mum died when I was young, Dad lives in another country, MiL has MH problems, and we rarely see FiL as he left when DH was 9.
I know it is hard, but I promise you it a walk in the park compared to being a single parent.