Hi there
I think you probably have a combination of things going on here. First of all of course is the new baby, she is probably going through a phase while she is adapting to the change. Definitely try to give her as much undivided one on one attention as you can manage, I know it is hard with a new baby.
Does she have all her teeth yet? 2yr molars could be contributing as well. Also, approaching 2yrs she might be experiencing some developmental changes as well. Things like leaps in language and comprehension can really affect behaviour and sleep.
Finally, I think she is OT. I know you said she needs a good run between nap and bed, but I actually think she needs a longer nap. 50mins is quite short for a 2yr old, and she has quite a long day especially if she is up before 7. I would either give her a longer nap, or try again for an earlier bedtime.
Was she previously an independent sleeper? When you say she coughs and makes herself sick, does she actually get physically ill? If this is the case then you will likely need to try more of a gradual withdrawl approach where one of you stays in the room while she falls asleep to begin with, and then gradually decrease the amount of time you stay with her. Here is a link with more info:
http://babywhispererforums.com/index.php?topic=80750.0What do you think?