Ruling on giving the expiation for delay in making up missed fasts to relatives
Question

I have a maternal aunt who is a widow and has no income; she lives on her own and receives some financial help from two of her brothers. I also have a maternal uncle who works but his salary is not sufficient for his needs; he has four sons, two of whom are studying in university. My question is: is it permissible to give them the expiation for delay in making up missed fasts (eighteen days)? How much is that expiation, and how is it to be given to them?
Praise be to Allah.Firstly: 
If a person delays making up missed Ramadan fasts, one of the following must be the case: 
1.His delay was for a valid reason, in which case he only has to make up the missed fast;
2.There was no reason for the delay. In this case he must make up the fast and, in addition to making it up, he must also offer expiation. This is the view of the majority of scholars (may Allah have mercy on them).
Some of the scholars (may Allah have mercy on them) were of the view, which is the second view concerning this issue – that what is required is to make up the missed fast and also to repent for the delay in making it up without an excuse. As for the expiation, it is not obligatory. This has been discussed previously in fatwas no. 122319 and 26865. 
Secondly: 
Expiation for delay in making up missed fasts – according to those scholars who say that it is required – is not offered in the form of cash; rather it is to be offered in the form of food which a person gives. What is required is to feed one poor person for each day. 
Shaykh Ibn Baaz (may Allah have mercy on him) said:
You have to repent to Allah, may He be glorified, for this great delay. What you should have done was fast the days that you missed before the next Ramadan came following the year in which you did not fast. In addition to repenting, you must also feed one poor person for each day, giving half a saa‘ of the local staple food, whether it is dates, rice or something else. This is equivalent to approximately one and a half kilograms. It should all be given to some poor people, or even to one poor person.
End quote from Majmoo‘ Fataawa Ibn Baaz (15/341) 
There is nothing wrong with you giving this expiation to your maternal uncle or your maternal aunt, so long as they are in need. In fact that is better than giving it to someone who is not one of your relatives. The amount in your case, for all the days in question, is 27 kg of rice. 
And Allah knows best.