Hey brother. I know you guys have been dealing with a lot lately, so this is pretty understandable, from both your perspective, and hers. I would try to talk to her about the motives behind you going to the gym (being strong for the family, getting a little "you" time and a release that will make you a better husband and father when you get home, etc.) I bet that when external stressors calm down a bit, it will be less of an issue, but for the time being (and I know this isn't easy), try to avoid the me vs. her mentality, and don't raise your voice when you talk about this stuff.
The is no reason you can't get to to fully support a healthy mental and physical activity like hitting the gym, but it make take little finesse.