It's difficult to have no contact when there are children involved and that's why we encourage posters to only contact them if it's an emergency or a need to know when it comes to the children.
It's called the distance/pursuer game that you two have been playing, i.e., when you stop communicating w/him, he begins to reach out and this will go and on until you stop it...but that's up to you because you can go dim w/him and not respond quite as often or as quickly when he reaches out.
As for the washer facet, if you are comfortable w/him being in the home, by all means let him come there and fix it. You can be in another part of the house or out when he's there... but be sure you put any important paperwork that you are working on away somewhere safe.
Just remember, you are the only one that can determine how much communication you want w/him on any given day.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.