I know it's harder for you and your father since your mother died. Have you looked into services for the elderly where he lives? Is their a local day care centre? What about a local retirement group? Why not see if you can chat to the public health nurse in his area or his gp as they will know about local services/organisations in your fathers area that could get him out of his house a day or a few days a week.
What about supported housing near where you live? He would live on his own but get support and could meet up socaily with other people living their?
You mentioned that you have a large mortgage so he would need to sell his house to cover the cost of this. Where does he live when your waiting for planning permission and the building work to be done?
Have you spoken to your dp about this? What age are your children?
Do you work full or part time?
Say your father sells his house and you don't get planning for a grand dad extension? If your father moves into your house until the building work is due how will it effect you, your dp and children?
Once your father is living with you even in a granddad extension he could be in your house a lot so you have no privicy as a family or as a couple.
I know a lot of eldery people and they want to stay in their own home. They don't want to move. Also most elderly people don't like noise so asking them to move into a house with a few young kids or loud teenagers is a lot to ask.
If he moves in with you it will effect you, your dp and children. You will end up considering granddad before you go away for a day, a weekend or on holiday's. Do you want to be bringing granddad with you?
Do you want granddad expecting that every time you go to the local town you will always bring him with you?
Say your father gets into bad health and he needs more care - what happens then? Are you able to give up work to mind him full time?
Have you siblings that will help you out? Will your siblings think your offering to let him move into a grand dad extension so you can get your hands on his money - when they are expecting an inheritance at some stage?
Rather that let him move in with you I would look into additional services near him. Get him more help in the house is garden done, online shopping, daycare and retirement groups..
I think that with your mother dying you know he is on his own for a long period of each day and he likes some company. So your driving their a few days a week which means that it's eating into your free time and time you could be needed at home. Your probably not seeing your friends either and you need dad and family free time for your own health also.
I know people who have taken on minding and or living with elderly parents. It's not easy from a physical, mental, financial or in regards to their own family or personal life. Some elderly people are grateful for the help they are given. I know other elderly people and no matter what is done for them they are never happy and continuous complain about everything.