I'm not going to notify my mom directly that my husband got a job in my city
Why won't you notify her? Don't you think she wants to know this news?
I don't want her to feel like I forced her son to move forward.
You should share that news with your mom. She would be happy to know about your husband's new job.
It is my responsibility to inform her and I'll do that when the time is right.
I hope you will do it soon. A parent would expect to be notified of such big news in your life.