Can you play a rent card and charge them rent? then a double the rent card on top of it to charge additional money
Yes, mostly. You double the amount collected in that one rent payment. Usually this is the same as collecting the rent a second time, but note that "Just Say No" would cancel the whole thing, not just the second payment, so it may be slightly different than you're thinking:
Play immediately after a standard Rent card to double the amount of rent collected. Can also be banked as money. Bank value: 1M. (NOTE: Playing this card along with a Rent card counts as two of your three possible card plays for your turn, per Hasbro).
- Playing a Just Say No card cancels both the Rent card and the Double the Rent card, per Hasbro.