Whether or not your landlord can charge you for rodent removal is less of a concern than the fact that he waited two months to make a claim against your security deposit.
Under Florida Law a landlord has 15 days to return your security deposit in full or 30 days to give you written notice by certified mail of the reasons he is making a claim against your security deposit. If the landlord fails to give the required notice within 30 days, he forfeits his right to any claims against the security deposit.
You need to send a letter to your landlord within 15 days of receipt of his letter objecting to his claim against your security deposit. If he does not return the remaining amount, you can file suit against him. Florida Law allows the prevailing party in this type of suit to recover attorney fees and court costs.
Feel free to contact me should you wish to pursue legal action.