Hello Milka,
as someone else has already described, the banks refer to ACTUAL conditions, i.e., the transfer to you and your sister must actually be completed in the land register before the rental income from the house is attributed to you.
However, there is also an advantage at this point if the newly acquired property actually has a separate granny flat for the mother (Check/present [Abgeschlossenheitsbescheinigung]!) - then the rent of the mother or the local customary rent can be applied. It is also possible that your mother-in-law becomes a co-owner of the granny flat (so-called partial ownership) and thus her entire income can be included in the financing. For this, it is definitely advisable to consult a tax advisor, because in my opinion you have - in the best sense - all options, including the deductibility of renovations and possibly even interest payments.
Also possible are usufruct agreements, i.e., you are the owners and your mother receives, for example, a lifelong right of residence.
So there are relatively many options that you should explore together with a tax advisor, because afterwards your search options for the property to be acquired may be directed/can be directed accordingly.
Best regards Dirk Grafe