Hi Girlsville,
Ouch - sounds like a real heart-string tugger.
Sounds to me like your DD is very attached to you (which is great) but maybe she's concerned that, when you leave, you won't come back (kids are kinda illogical like that). This may be especially accute given you've got a new baby around the house ? going from 24/7 Mummy attention to, at best, 50% of that is hard for kids.
When you put DD down for naps, is it always you that is there when she wakes up too? I'm just trying to think of it from the point of view of an hysterical 2-year-old who's thinking "I can't let Mummy leave, or she'll never come back!" - do you always 'come back' as it were?
Another possibility is that it's a bit of a power struggle. My DS1 had a similar thing with my DW. In a nutshell I was 'bad cop' and when I put him down, unless he was in serious distress I didn't go back. My DW tended to go back to him more often if he was upset - so he learned that: crying was kinda pointless with Dad unless it was really bad; and that 'Mummy comes back if I cry'. This is a pretty powerful lesson for a child having that 'power' over a parent.
Is it possible you could get some help short-term around nap times? What DW and I did when she put DS1 down was - once he was down IF there was a lot of tears, I'd go and check on him.
This breaks the 'power' link from child to Mum; but also helps reassure the parents that the "What if this time he/she really IS upset/hurt/on fire?" worries are just that - worries.
Basically, what you want is for DD to be reassured, laid down again, given a little comfort (if needed) after you've put her down and that's it. Then, at the end of naps you can go in all sunshine and smiles to help reassure her that Mummy always comes back in the end - so no need for the dramas.
It can be really hard to sit on your hands whilst someone else checks on them, when every instinct is telling you to charge up there and check they're ok. But it's worth it in the end - for you and her.
Hope that helps. Good luck!