Property Boundary Dispute

TL;DR. How do we respond to the owner next door who claims we are impeding on their property by cutting down trees and trying to replace damaged fence after we hired a licensed land surveyor who confirmed that the trees and fence are on our property?

How do I legally respond to the owner of the house next door

Location: Georgia

Background info: we closed on a 1993 house over a year ago and have yet to move in due to renovations. There are multiple trees along our driveway that were dead/dying that we felt needed to be cut down before they fell onto our house. The day after the tree company cut ~15 trees within our fence line, the sister of the owner (who claims to represent the owner) shows up pissed, claiming we cut down their trees, threatened to report us to the county and hire an attorney.

This is the first resale home we purchased and didn’t know better to get a survey at closing. We decided to cut these trees down because we never even questioned those trees may be the neighbor’s next door because it was clearly on our side of the fence.

We ultimately hired a licensed professional land surveyor and learned that our property line extends 18” past our fence line. The fence is dilapidated and multiple parts of the fence have partially fallen over due to dying trees that were leaning into it. We ultimately want to replace the fence but now we want to move it and claim our property based on the survey.

We recently received a letter from the landlord’s sister in our mailbox requesting that we stop crossing into her property and altering the landscaping until she gets a survey. The letter was literally an email between her and an attorney with an aol email that we believe may be an attorney friend who helped draft up the letter and she was suppose to send certified mail. Instead, she printed the email containing the letter signing her name and contact information in the letter but the envelope was written to be from her brother, the owner of the house next door. There was no mailing stamp on it so clearly, she came by and put it in our mailbox (clearly NOT a certified letter). She is foreign so that may be why she didn’t know better than printing the actual email nor knew how to send certified mail.

We want her to get a survey so we can settle this altogether and move on with our lives but we don’t want her to drag her feet in getting a survey as the tenant have suggested the owner/sister are very cheap and never want to repair anything in that house. We thought about finding the actual address of the owner (her brother who lives out of state) and sending a certified letter to him providing a deadline for them to complete a survey or we will proceed with replacing our fence. However, we would like to handle this cautiously. Are there any legal nuances that we need to consider in taking this approach? We are not sure if we are at a point where we need to hire an attorney.