we have always found it hard coping with medical emergencies around work etc etc.
What kind of medical emergencies? If my mum (elderly, very frail, housebound) can't get in contact with us she knows to call 111 who will advise and get emergency help if required (out of hours GP home visit, ambulance). She had paramedics out last week checking her over as she felt breathless, dizzy and anxious.
If she calls and is worried about something and I can't go over (in work and can't leave, at a kids party, dh working and have to pick up ds, I did the last mercy dash etc) I'll tell her to try one of my siblings and if they can't come to call 111.
She does go through periods when her health deteriorates or gets serious (lymphoma returns) and it needs extra effort from us to attend more appointments/visits in hospital for a while and we sort out fair share with my siblings (apart from one who doesn't want to get involved), but when she is at home we don't let her get dependant on relying on us entirely or she would have one of us there 24/7.
General appointments at gp or hospital/dentists/opticians etc she is told to organise and go herself and it is explained as we all work FT have families we can't afford annual leave for routine appointments and she needs to accept that (she has plenty of money for a taxi to these appointments door to door, uses the local firm who know her and they make sure she gets in the door ok). We found making her organise it herself has given her a bit more confidence do it.