In Islam, when a man passes away, his wife practices a ritual called "Iddah" (in Arabic). In this practice, she is not allowed to marry another man for a duration of 4 months and 10 days, not allowed to get out of house, wear makeup or bright clothes. This term is generally referred to "waiting of a widow" so I wonder if is there a single word in English language which clearly means "Iddah"?
The English term would be the Christian equivalent: mourning. Iddah could be quickly described as "Islamic mourning" or "Islamic widow's mourning".
As @Prof Yaffle mentioned in the comment, I don't think it is meaningful to find or use an English equivalent for Iddah as it seems to be a unique practice in Isalam.
Mourning in the Western culture doesn't include restrictions such as not being allowed to go out or wear make-up.
You should stick with "Iddah" and the Wikipedia article uses "period of waiting" for it and I think it is closer than just "mourning".
Or "(Islamic) period of mourning" would be more appropriate.