I'm dealing with something similar...I have a 3-year-old and a 7-week-old and trying to pay attention to one at a time inevitably ticks off the other one.
Telling your toddler, "If you can't be gentle (quiet/respectful/whatever) with the baby, I will have to separate you" is absolutely reasonable and your husband's opinion is only relevant if he is present to distract the toddler for you. So no, I don't think putting your toddler in another room for five minutes is harmful.
I know my older daughter gets more obnoxious and aggressive with the baby when she's tired herself and/or desperate for my attention. Good or bad, it's still attention, right? So I scold her, and she throws things or herself, or runs off and sulks, or shrieks at me. It's an unfortunate cycle and sometimes separating the kids (or letting the older one run off and sulk--she usually goes in her room to read) is best for all involved. Then once baby is calm or asleep I can do something one on one with Rowan--bath, books, whatever.
Amelia, married to Bear since 12/31/04; our daughter Rowan was born 8/6/09; our daughter Sapphira was born 8/17/12; due with DD3 6/17/15 (but after one two weeks late and one three weeks early, I'm not expecting a due-date baby!)