Hi!
We splitted your question into a separated topic cause it seems that there's a lot going on and in a separated thread you might get more replies specific for your case.
I think what's happening here is a confusion with your dd.You say you've tried everything from 2 months ago, including a major change like switching her to a toddler bed. So now she doesn't know what's expected of her and what she should be doing. Possibly the added stress (the one that you're feeling and the one that she's feeling) of a coming sibling is not helping much.
So, first advice, relax. I promise we'll get her back on track by the time little sibling arrives. I know it's easier said than done but you can do it. Take a deep breath.
You mention that she'll eventually go to sleep with the gate so I'm gonna focus on advice related with it so we stop switching methods.
There's also a mix of overtiredness here due to her short nap and her early mornings so is sort of a vicious cycle we have to break somehow.
My first advice would be bringing bedtime super early (such as 6 pm) considering she's taking a lot to finally go down. Try to get her on bed by 6 pm and if she goes easily GREAT, she'll catch up on lost sleep. If she doesn't go that easy, well at least she won't be that tired by the time she actually goes to sleep.
Then, as soon as you've done a long winded and relaxing wind down routine, tuck her in bed, say bye bye, kisses cuddles see you tomorrow and out you go. She'll probably jump out of her bed or cry for you, the first time you redirect her to her bed and explain briefly and calmly that it's bedtime, we'll see you in the morning i love you and out you go. Then is your choice if you get out of sight or stay at the door. I'm thinking it'll be better for you to get out of sight so she knows is not playtime and will stop getting out of bed just to get you by her side. If she climbs out of the bed but doesn't cry for you, leave her be... she'll go to sleep when she's ready. Only walk in and put her again in bed if she tries to leave her room or cries for you.
Do the same for naptimes and stablish an early naptime while she takes long to go to sleep to avoid overtiredness.
For early mornings, I'm hoping these ones get solved once she catches up on lost sleep. If not, do the same, redirect her to her bed, explain briefly the first time and leave. Following redirections should be made without reactions from you (not anger,not desilussion, no pity... just take her to her bed, i love you bye bye).
I HTH somehow,it is such a tough and stressing thing. I can totally understand how you feel but i can also guarantee you that if you keep consistant you'll get trhough it. Good luck!