Can you play a rent card and then a double the rent card?
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.
  


Quoted from https://monopoly.fandom.com/wiki/Monopoly_Deal#The_Cards_In_Detail