How to get client to pay what she owes promptly if possible, also do I have a strong case for court i.e. small claims??

Hi I'm a self employed handyman/carpenter who lives in PA and did said work in MD. I built a large horse farm fence for an older lady whos a racehorse breeder. She signed the contract for the work which stated the est project completion time would be 3-4weeks. During this project she asked me to stop fence work and build a shed, which I did. She asked me to stop and rehab a barn which I did. She then says initial fence job is taking too long and asked if someone else can finish the rest, to which I agreed. 4 Days later she text me back and asked if I could come finish fence because the other "contractor" only knew how to do a small part and wasn't experienced enough. I came back to finish fence and completed it.. Fence looks great and she is happy with the fence, shed etc... On my last work day there she says to me that the fence took long causing her to board horses longer than expected and she says she will only give me 8k instead of 13k because of this. She never had a deadline on our contract. It only said estimated time 3-4 weeks for fence job. If I subtract the time that she took me away to do other projects etc.. then the fence took 5 weeks. She agreed to barn contract through text msg but we only have a verbal agreement for shed, but I have witnesses and pictures of me and crew building it etc.. We talked a few days after fence was done and she doesn't want to budge and she says I guess you'll have to take me to court, but its expensive. How should I go about getting her to pay what she owes for the1700ft long fence etc etc I built her? Thanks in advance for any advice, Steve