My 89 year old father has fallen several times, My stepmother tried to help him the last time he fell and she herself ended up very sore and afraid that she would hurt herself. She thinks she should hire a young man to accompany my Dad when he is out. But I don't think this is a good idea since the situation then puts the young man in danger of getting hurt trying to prevent a fall. Neither my dad nor step mom seem to be ready to face the fact that my dad may not be able to go out to places with out a cane or walker. The reality of the situation is that he will fall unless he is in a wheelchair and they might have to curtail going places. I do not know what to suggest to them to keep my Dad and step mom safer.
Eventually, they give in. Your's will too.
StepMom should not try to get him up. In many communities the local fire station may be called for help getting someone up off the floor or out of a bathtub, etc. Check this out in their locality. Also, PT may be able to give Dad some tips for getting himself up.
StepMom would be justified in saying "Dear, I'd love to go out to dinner tonight. Would you be willing to use your cane (or walker) so I don't have to worry so much about you falling?" And if he says No, then "OK. It is up to you. I'm sorry, though, that I'm not willing to take the risk. We'll just eat at home tonight." His kids could follow the same practice. This should not be argumentative or sound like a punishment.
How does he feel about a wheelchair? That is generally the safest bet. My husband was perfectly OK with that, but hated a walker. Go figure. If he is willing to be pushed in a chair, a transport chair is the easiest to get in and out of a trunk. Also many places such as museums, botanical gardens, and other public exhibits have loaner chairs.
It would be a real shame for Dad to be isolated because of his mobility issues. There are ways to reduce the risks, if the parent is willing.
Beyond that, you will have to accept that you cannot make him absolutely safe. Unfortunately it may take a severe fall for him to realize the value of being safer.
Good luck!