I'd have no qualms about sending her in more. Don't feel guilty. When the baby comes, nursery is a valuable baby-free space!
However, I don't think that's a solution to all behaviour issues - you do need to find a way to feel on top of things rather than defeated by it. Nursery can't sort it all out for you and if her behaviour is poor at nursery that causes problems too.
How pregnant are you? Have you tried talking to her about the process, reading books with her etc? She might be unsettled by you being less mobile, more tired etc but if you show pictures or make a little book of what will happen, how you won't be this way forever and she'll always be special and part of your family, it might help.
With tantrums you need to do all you can to minimize (routines for snacks, sleep, activity etc) to help prevent her being overwhelmed and give vocal warnings 'we will do this in two minutes, one more minute of playing' etc.
Praise good behaviours a lot and tell her she's a good girl etc. Screaming, refusing to get in pram you can wait it out so long as it's not dangerous. Things like pulling car fur and drawing on walls would be absolute scorched earth unacceptable to me, very firm voice and she goes on the step or toy taken away etc - immediate consequence. They sound kind of like attention seeking things though.
When you say you've tried techniques - how long for? It can take a while for something to take effect.
I had dc2 when dc1 was 2.5. it was hard but survivable! Having a place to put the baby in our main rooms (high chair, bouncer, sleepyhead type thing) helped as I could pop baby down and sort dc1 out if she was acting up, and give her more attention while dc2 watched us.