Shalach Manos and Aveilut Rabbanit Rachelle Sprecher Fraenkel

I am so sorry to hear of your terrible loss. This must be a very difficult time for you. Please note the specifics of your case, after the general discussion.

One of the laws of aveilut is limiting the way people greet and inquire about a mourner’s welfare during their time of grieving – starting with the shiva and to a different extent for the full time of their status as a mourner – a year for a parent and 30 days for other relatives.

Sending mishloach manot is considered a warm and joyful way of greeting
 .(שו”ת מהריל ל”א , שוע” או”ח תרצ”ו ס”ק ו’,יו”ד שפ”ה ס”ק ג)

Accordingly, the Rama and Ashkenazi minhag  instruct not to send mishloach manot to a mourner as long as they are in their aveilut status.

The mourner himself is obligated in the mitzvah of mishloach manot and should give one (even during the shiva). It is appropriate to give mishloach in a more modest manner than the usual festive way, sending only the obligatory one, containing food and not sweets etc.

Sephardi ruling on this is different: aveilut is overridden by the Purim holiday, hence one is allowed to greet the person who is still in the period of mourning.
Therefore the Sephardi costum is to send mishlochim to a mourner.
.(שו”ע יו”ד סי’ תא ס”ז, חזון עובדיה פורים ואבלות)

In any case, it is permitted to send mishloach manot to other family members who are not in mourning, with the knowledge and intention that the mourner is going to enjoy them too.