Yes for TV but not for internet. Satellite TV will come from DirecTV or Dish but internet will need to come via some cellular provider. This will NOT be anything close to what you now have assuming your internet is provided by your cable provider. That doesn't mean it will be bad but it will be slower and it will be location dependent. It will also likely be more expensive for less with data caps that you don't have to deal with from a cable provider.
You can setup either satellite service at both houses with antennas permanently mounted on the (assuming you have a good clear view of the Southern sky) and then you will need another antenna for the RV, either self pointing or manual and either roof mounted or portable. What services you want will make a difference in which antenna is required to meet your needs. You will then be able to move the receiver from home 1 to RV to Home 2 and back again as necessary.