S.H.
She's in the "terrible 2's" stage, she's a runner, and very active. My friend's boys were like that too, and my son is like that too. I can relate.
Sometimes all the nipping in the bud you do, will or will not work. BUT, being that you are pregnant, I would take safety first. Use the harness... sure, they will pull on it wanting to go in all directions.... but don't give in. Use your voice and show her that you will NOT give in. At least for my son, he has learned that. OR, simply leave her at home with someone so that you can do errands, even though she may protest about it. With the baby coming... I would surely get a "plan" set up so that you have a back-up helper when you need to go on your OB or well baby appointments in the future. LOTS of Moms do this... do not feel you have to go it alone. Or, there are delivery services that will do grocery or other "errands" for you. Check your area for that. Or, simply go on your errands when Daddy is home... surely he can understand. It's perfectly reasonable.
Do you have your family or his family in town? Enlist their help. Talk to them ahead of time, so that everyone will be on the same page about it.
As for the tantrums/screaming they do at the worst times while you are out... you can't give in. Or distract her. But don't use "treats" or bribes... otherwise they will think that any tantrum will bring them treats. I simply tell my son, who is almost 2 yrs, old, "no" and if he keeps yelling then so be it... but I don't give in. I also explain to him what I want him to do.... ie: "you must sit in your stroller while Mommy is in the store...then I will let you out...." and he does understand this and will do it. It takes repetition. If they see they can wear you down, they will.
Or, tell them that "Mommy needs help... we don't yell in stores... if you do we are leaving." At this age though, they are still learning social rules and do not have full impulse control yet.... but they do need to learn boundaries.
I know it's hard... and with the baby coming and all. But enlist help for yourself... there is nothing wrong with that and getting an extra pair of hands to help you. If anything, and if you can afford it, get a "nanny" to come to your house...to help. The "toddler" phase is not an easy one for sure!
It will pass though.
All the best,
~Susan