Headphones, if you're working on a track or something, then import that into a DAW.
I used to have problems with my neighbour, very similar to your's because my neighbour is annoying and used to have screaming arguments with her daughter. I now have my studio on the other side of the house above the garage on the opposite side of the house to the party wall. I don't use an amp unless I'm teaching, I use my monitors or headphones. I'm often working on pieces that I'm writing until 3 or 4am, nobody notices, not even my parents.
It's very easy for these things to get out of hand, and the noisiest neighbours are often the first to complain.