Good news/Bad news
Congrats on the babies!!! I would wait a few weeks prior to handling the babies. The mother won't like it and may bite you. Things should cool down after about 2 weeks.
It may have been a good thing to separate the male and the female. Some animals make good parents and share the parenting while others don't. Rats are good parents but I would monitor their behavior if together. It really depends on their temperment. Yours don't sound like they have that right now.
If you do have to move the babies then use rubber gloves. It should reduce the human smell on them.
The bad news I mentioned in the heading. A friend of mine raised rats. She informed me that the female rat is capable of impregnating herself with the same male sperm to up to 2 years. That means that your female rat doesn't have to be around the male to have another batch of babies in the next few months. So don't be surprised if she does have another batch in a year.
Rats can make good pets. However, they do breed too much and can be hard to adopt out. So I hope you enjoy having many rats or friends with many snakes!
Scooby, Shaggy the "Dogs", Ms. Thang the "Cat" and introducing Measley Weasle "The Ferret".