It's not very clear, is it your partner's brother and his wife who drive or your partner, brother and SIL? Sorry, please don't take that as a criticism as I know you are upset and typing on your phone but just wanted to clarify.
If it's your partner yes he should be driving you. Have you been over the weekend? Did he drive you then? Is there a reason why they can't help? I know some people might have their own work or childcare commitments which mean they can't do things at particular times, particularly if brother and SIL don't have another grandparent their kids can go to.
If it's your brother has he visited her at all? But perhaps at a different time of day? Is he maybe thinking that it's better that you go at a different time from him so that your mother has someone with her as much as possible?
If it is your partner's brother and his wife that you're expecting to help out, it would be nice if they would, but they're not really obliged because it's not their family.
But if it is your partner, brother and SIL, I agree with the other posters, you may need to sit down and talk. It will be a stressful time for your brother too so don't go in with all guns blazing, they may be struggling to get there too with their own commitments.
And practically, at the moment, it may well be best that your mother has someone with her for as much of the time as possible. You don't mention if your father is around or if she has a spouse on the scene. But you may need to consider if she is really very poorly you might need someone there for the doctors and nurses because things can change quickly and decisions might need to be made. Possibly if your brother can cover some times you can't so there is someone with her most of the time then the bus journey is a reasonable price to pay?