Your mother wants to retain ownership of her house
She wants you to pay to have the house renovated, build an extension and move in.
On her death she plans to leave the house to you and your sibling.
On her death you plan to take ownership of the full house.
You don’t have the cash so you needs loans for all of this.
Say the house is worth €300K and you will need to spend €100K for the upgrades and extension.
You spend the €100K, which is essentially a gift to your mother.
She dies and leaves the house to you both, essentially €200K each.
You then spend another €200 K buying your sibling out.
I can’t see any regular bank lending you the €300k you need for this. And I know nothing about trust/probate loans. If your mum is elderly, say 75, you are probably 50 and would you be able to pay back a €300 K loan over 15 years, which would take you to 65 and when you stop working. You will need to do the calculations yourself. And maybe talk to brokers etc., would you have 10-20 % saved already? Because it is not a mortgage the interest rate is higher too. And even if you wanted to take out a €100 K loan first, who would lend you money to refurbish a house you do not own?
It would be a lot easier if your mother sold the house to you for €300K, she spent €100k on the renovations and gave the €200K to your sibling. Same outcome, much easier to do. But there are pitfalls with this approach also. What if this all happened in 2024 and your mum needed nursing home care in 2026. Her assets would be considered to be the €200K she gave your sibling plus a value of the right to live in the house. Or she might be assessed as having assets of €300K so this could be a significant risky move for her and her estate.
And overall I wonder if you would resent your mother and sibling if you end up with a €300K loan and your sibling ends up with €200K cash.