I have walked this path before you and know and understand how agonisingly lonely it feels, as if a whole part of your own life has been wiped out e in the process. Clearing out the parental home is emotionally tough, being so full of familiar things. You just have to plough on through until the task is done and be grateful for the memory of happier days. All I can say is that your parents worked all their lives to provide security for themselves. Whilst the house has to be sold, at least it will be providing some security in the form of residential care for your mother. If she has had to be sectioned for Alkzeimers you may find that she actually may not have to fund her own care fees so check with Age Concern or some other caring agency. The Fact Sheets on the Age Concern website may also prove helpful to you in terms of giving detailed information about what funding your mother may be entitled to, i.e. Attendance Allowance, etc.
Could you have her moved to a care home nearer where you live so that contact is easier? Meanwhile, you are still grieving for your father. Having such a big burden still to tackle is hard for you, so take whatever time you can to make a little calm space for yourself, even if it means taking a short walk somewhere pleasant to reflect , unwind for a moment and draw enough courage to face the next day. There is an old Russian saying "You must eat the elephant piece by piece". Break down your tasks into manageable sections and slowly you will find that the fog is clearing and you can see the light for the trees. .