Need some help or perspective

I am wanting to get a gym membership and go after work for an hour. Here are our schedules.

Husband works 5 AM-3 PM

I'm home with the kids during the day and work from 4:30PM-8:15PM

I'm frustrated in the expectations I'm a stay at home mom when I'm not I also work. I do everything. Currently I'm dieting and lost 15 lbs and I'm partially handicapped with and autoimmune disease so I can't work out hard Im 285 lbs and really want to be healthy. I have a recumbent bike however I can't workout after work at home. My husband won't put the kids to bed and won't clean up after dinner. By 10:30 I'm exhausted. I feel like if I went to a gym he would be forced to step up. I'm tired of communicating to him I need me time. Weekends I get none. I legit only get a break at work and even then I'm in a physical and mental exhausted job (that I like and need for my sanity.) We have no extra money for help or family to rely on.

I found a gym for 10 dollars a month and I feel like telling my husband this is now the plan instead of asking him. Whenever I communicate about him doing more a d being direct with what I need he tells me I have a "victim mentality" that this is my job and I signed up for this life.

Need to emphasize I do all the cooking even dinner before I leave for work and pack his lunch and breakfast. I do all bathtime. I basically set him up for an easy night with the kids. I think it's reasonable he put the kids down to bed or do dishes before I come home. Is this unreasonable?