It can be a grind at that age - I'm so sorry that you are having a hard time. You aren't a terrible parent at all - just a very, very tired one! It's hard to be enthusiastic about anything when you are living with that sort of sleep deprivation over an extended period of time.
I agree with the poster above that if you can manage it, take him out every day. Mine at that age I thought of like a puppy - if I didn't take him to the park twice a day and wear him out there, he'd chew the sofa and eat all our shoes...
On the behaviour thing, blimey, this is pretty hard. In the end, the thing I found that worked was, if my DS at that age kicked off, I gave him three chances to calm down, then I marched him home. Didn't matter what we were doing - in the park, in the supermarket, in the playgroup - once I'd counted to three and he was still misbehaving, I'd put his coat on and march him home, no further chances. It was HUGELY inconvenient at the time, as more than once I left a full trolley of groceries in the supermarket as he'd kicked off, and there were other times where I took him home halfway through tea at someone else's house (the other mums supported me doing this), but it worked. Once it had kicked in, I just had to start counting to three and he'd pay attention.
I never punished him beyond just marching him home - the leaving-the-interesting-thing was the punishment by itself. The only way this works is if you are ABSOLUTELY consistent - never ever threaten it and don't do it - once you start counting down, you have to follow through. It might not work for you, but for us it really, really worked. (And of course it's no good if you are already at home and he kicks off.)
You say your OH is working a lot, and you work 3 days a week. Is there a chance you as a family might be able to afford someone to collect your DS from nursery one day a week and take him to the park for a couple of hours, just to let you catch up on sleep, or at least get home from work and not have to go straight into mum-of-a-toddler-mode?
Anyway, it does get better, and someday you WILL have a full night's sleep! There will even come a point where yours is old enough to make you a cup of tea! In the meantime,
and
.