I do not understand why the question cannot be answered clearly, distinctly, and above all, comprehensively.
Basically, with the income, a mortgage-secured loan in the desired amount is not a problem at all. Anything other than a mortgage loan does not make sense. It would be too expensive, too large at over 100,000 euros, and, as described, completely nonsensical. If a land charge cannot be registered, I would also not carry out the value-adding expansion and modernization.
The mortgage loan must be secured by a land charge on the parental home. Thus, the parents are liable in rem and the [TE] personally. A purpose declaration that the bank requires from the parents on a form then establishes the connection between the loan and the land charge.
It is important to know whether there is still a valid land charge or whether the house is free of encumbrances. A land charge that is no longer valid can be assigned to the bank. Otherwise, the land charge must be newly registered.
If the house has a granny flat, taking out the loan can lead to the local customary rent no longer being recorded as income by the tax office. Consult a tax advisor on this. The question remains whether rent is currently being paid and, if so, whether it will still be demanded or required for the parents after the investment.
So, a mortgage loan secured by land charge based on the parents’ security is possible and feasible; the purchase of a kitchen and the repayment of existing loans can also be realized with and from the loan.