A couple thoughts. She's probably too young to be potty trained. True potty training happens when a child is able to recognize they need to use the potty, and they are able to hold it long enough to get there. 21 months is awfully young to do that, although some parents achieve that by frequently making the child sit on the potty - which does achieve the goal of clean underwear, but isn't really potty training.
It does sound like your child will have a bit of a difficult time, since she was uncomfortable with you holding your niece.
But I have to ask - what specifically do you not want about having two in diapers? Is it the expense? If you're thinking it's more work to have two in diapers - it isn't. The hardest thing is to have a newborn and a child who is barely potty training so that you have to be one minute away from a toilet in all situations. That's hard. Diapers are super easy.
Lastly, if you're pregnant now your children will be 2.5 years apart - that's not really "having babies close in age". That's kind of the longest distance you can have them apart and still have them kind of grow up together. Any further apart and their interests and abilities put them into two completely different peer groups. Which isn't necessarily a bad thing.