Next month my niece will have her baby..but she is 341 pounds (after 3 months of dieting) what should her weight be?

A lot less: I would be curious as to why you are asking. It seems fairly obvious that she should be a lot less. But, she knows this already as well. Perhaps she can discuss bariatric surgery options with her physician once she is delivered.

Depend on her age: Height and constitution. No more then 180 lb, i guess.

Weight loss of 1-2/w: is considered healthy and safe, and with delivering the baby, there may be an additional weight loss of 15# or more from delivery of baby and placental weight, etc, so in 3 months, if she is less than 300 #, she should be pleased with her progress.