Buyer: obtaining security deposit and pro-rated rent from seller?

[Gray Diffee]

Closing day is less than 2 weeks away! This is my wife and I's first RE investment and we could not be more excited! I contacted the sellers agent directly and she has been representing both sides. Not a great experience doing so. But we DID in fact get the deal done because the agent was willing to give up some commission. So, all in all, I can't complain. But I certainly will find my own agent from now on. 

This brings me to the issue at hand. dealing with the sellers agent has been a little sticky. So, when I asked the agent about how the deposits (its a duplex w both sides rented)  was going to be transferred, as well as the pro-rated rent considering we close a few days before rent is do, she did say that the deposit will be handed over to the new owner (me) at closing, but seemed irritated about the pro-rated rent and even stated "its only 1 day.." (correction, it will be 4 days between closing and the next rent due, which adds up to $270 of rent) 

Im looking for a simple and professional way to handle this. This is our first RE investment, so, I am still learning a lot. I absolutely could be out of line here. But this seems so basic to me.. How have you others handled this in the past? Anything legally binding on either end?