Can an Aveil for a parent give presents to her grandchildren? Does after 11 months make it more lenient?
Normally it is not permitted for an avel to give gift during the aveilus year. However, it is permitted for the avel to give gifts in situations when it is not merely for simcha, but it is expected, and derech eretz to give the gift. For example, a bar mitzva present, or wedding present are permitted to give for this reason. He same would apply to giving a birthday present if the relationship between the two is such that it is expected that it be given. The same would apply, to a grandmother giving a Chanukah present to her grandchildren, if this is what she usually does, and it is expected. Then it would be included in derech eretz, and permitted.
Have a happy Chanukah