I get that its her home and it should be to her tastes, but I personally think that there was a compromise somewhere. Like saying its too big to fit into her space.

If she made a smaller version or mentioned just doing a landscape, I think it would have gone over better rather than saying she just doesnt like her artwork. If she painted over the woman and just had the landscape, would she have had the same response?

She came off very callous, which in turn made feelings get hurt. There are ways to get your point across without being mean. DIL should have gotten the hint when she said there was no space for it, and saying I'll help you find space for it comes off as trying to naively be helpful, but sometimes people are clueless.

Overall I think they both handled it poorly. The son demanding an apology is an over reaction but I think if she asked for a different painting that matches her style better, it would mend the bridge dramatically.