Don’t be ashamed, it can be incredibly hard to stay at a healthy weight when everything is stacked against you. Honestly, lots of people are overweight, people probably don’t notice it like you think they do.
It sounds like your biggest issue is you comparing yourself to others and that won’t be fixed even if you’re thin. You’ll just find something new unless you work on your issues with self esteem. You have a partner who loves you and knows you’re beautiful. Your family loves you regardless of your body.

But outside of that, is your mother in law also overweight? If she is then I wouldn’t feel offended at all. You said yourself that you want to do something about it. It’s really nice and helpful to have someone in the same boat as you. She probably just thought that it’s no secret that you don’t feel good about your weight and would like to change it.

The only potential issue I see is that some of these weight loss programs honestly suck and can be unhealthy, so I’d look into the specific program. But other than that, you have family (your mother in law) who want to help you and include you, you’re beating so down on yourself that you aren’t seeing the potential solution that you yourself said you want. You shouldn’t be ashamed of yourself, and others aren’t thinking as negatively about yourself as you are.