This makes no sense at all to me. You are now grown with a family of your own for whom you're responsible. Why do you think that you should follow your mother even if she were making a logical choice to move? If her health is such that you need to take care of her then she needs to stay where you are located. Your first responsibility is to your husband and your children.
Your mother asks you and your husband to give up your jobs and your friends and everything else. Does that make sense or even show love for you? Here are some practical considerations. How will you support yourselves? How will this emotionally affect your children and yourselves? How can you become an independent adult with an independent family if you continue to let your mother determine where you will live?
Your mother is an adult and if mentally competent she is free to make her own decisions but she is not being fair to you and your family to ask that you center your life on her. If she's incompetent and you fear for her safety consult a geriatric psychiatrist and/or a lawyer and consider going to court to gain control of her actions.
Why is your mother still in charge of your life? To me, although this would be a painful decisison, it would not be a difficult one. In a way I have had a similar decision. My mother wanted me to leave my family and move in with her. My brother was already living with her. I asked her to move in with me. She angrily refused and went back to her own home. This did change our relationship. It put an emotional distance between us but I believe that I did the right thing.
I was able to do this after therapy which helped me to recognize that my mother and I needed to set and keep some boundaries. Although we loved each other and had some reponsibilities towards each other because we were family, she and I had different lives with each of us having primary reponsibilities for our own life and not the other's. If I had moved in with her, to take care of her, abandoning my own family, we would be mutally dependent on each other and this is not a healthy relationship as mother and daughter. By choosing to stay with my family I was accepting responsibility to see that she was safe at the same time I was accepting responsibility for my own life and the life of my nuclear family. Once I reached adulthood and formed my own family this family was my nuclear family and my parents and siblings became my extended family. We are still family but the boundaries shift.
I do sympathize with your predictament. You want to help your mother. You want to make her happy. You want her to be safe. But I don't see how separating your family will in the long run help anyone and has a great potential of doing much damage.