Renting a car from one country and dropping it off in another is generally allowed by major companies such as Europcar, Sixt, etc. From Europcar's FAQ page:
"If you want to return the vehicle to different station from the station where you start your rental, [...] Domestic one ways are generally possible inside the same country between all stations, except between mainland and islands and vice-versa. Europcar operates a large network of international key cities in order to allow flexible cross border travelling. In smaller locations you will be required to pay a higher price."
The only thing is the prohibitive cost this will have, as you will effectively be billed for repatriating the car. So do call your agency in advance and check if this is an option for them, and for you in terms of viability.
I don't know about taxis between the two cities, as I am not a local. But you might want to check the cost and availability of local trains/coaches. I bet that will be cheaper than an international car-rental drop-off.