Hi L.,
I think that some babies just don't do well in a playpen. My first really hated it too. I personally let the baby follow me around while I clean. I just talk to her while I work. She usually does cry, but at some point they do have to realize that you can't always be holding them. When I cook dinner, I put the gate up by the kitchen, and the kids will sometimes stand there and cry (even my 4 year old). If their needs are met, then I'd rather teach them young that I'm there for them, but sometimes I have chores too. :) I also would suggest distraction if the crying is driving you crazy. I give my year old a little start to her dinner, and put her high chair facing the kitchen. She is usually fine there. So I guess it boils down to. Do what you need to do. Try the crib, playpen, gates, or whatever. You could work for 15 minute intervals so that the baby doesn't get too worked up. She will adjust, and then, hopefully, she will be a more tolerant toddler :)