An obvious thesis for an essay on Welding with Children is the thematic idea of beginning again. Bruton has two ideas for beginning again, one involves packing the kids up and heading to the Northwest to start all over again. Another idea is given to him by the man he consults, the man who called Bruton's car the "bastardmobile." This idea has to do with cleaning up physically and spiritually. Some story points involved are (1) how the townspeople talk about Bruton and the children; (2) how the children themselves talk; (3) Bruton's emotions in the face of these reactions and words.
When I read the story I identify the elements of the cruelty of people. The grandfather is spending time helping his daughter's with his grandchildren. He is aware that none of his daughters are married and each has a child, but he accepts and loves the children. He actually takes on a big role by taking all four at once and agreeing to watch the baby overnight.
When he goes to town the grandfather's vehicle is referred to by the two men as a bastardmobile. One of the children hears this. For me, I would be looking at the behavior of the men and attitudes as they reflect on the children and cause hurt through their words.
However, I very much liked what the previous editor wrote and I agree with her point of view as well.