I suspect that
a. Your family is just afraid you'll fall.
b. And some families know they can't leave work and take care of you. And some families just aren't willing to.
c. And families have read that if you fall you may never be normal again.
This new PT has given me an amazing number of balance exercises, and I'm amazed at how quickly they gave me confidence. A few weeks ago, I flunked a balance test -- my score said I should be using a walker (I assured them that a walker was not going to happen.) Two days ago, I was on the edge of the top category, which would allow me to go without a cane.
Here are some suggestions:
1. Demonstrate to your family that you will be careful in exercising. If you should use a cane, use it! If you get careless and fall BEFORE you even start exercising, can't blame them for saying "See! We told you so!
I went to an expert for safety comments, a woman who trains blind people to get around.
She tells them to pay attention at all times.
She tells them not to get distracted when they walk
2. Insist on some excellent physical therapy (wish I could send you to mine) And medicare will cover most good physical therapy for a specific number of sessions. Mine does!
Ask if the PT gives a certificate at the end of the sessions. (Families love visible proof like certificates.) Show them some photos of people exercising, even the e seated tai chi.
3. Have your doctor WRITE you a prescription (not a note) for PT or specific exercises and hours per week. In our area they even offer seated exercises to use in addition to your regular walk (if you don't hate being seen at a senior center.)
4. Actually DO your exercises. Introduce your exercise buddy to the family, so they know someone will be there to grab you if you goof.
5. If the family still panics: Start with simply walking (that was my RX after acute spine rehab.) I don't think seated exercise is enough, but then I'm the one who keeps pushing those Bed-cercises - things I learned in acute rehab after spine surgery, long before osteoporosis - good exercises you can do in bed before the rest of the family wakes up.