Does this letter to our adopted Grandmother make sense?
Any native Chinese speaker can edit and make your letter perfect and native sounding, however, that would not be your writing and won't help your learning. Instead, I would suggest some basic improvement.


  紅紅感冒 



since Chinese grammar doesn't have tenses, you have to indicate  Hong Hong's is "currently" having a cold by putting "現在"(now/currently) in front of the verb.
If you treat 感冒 as a noun, "紅紅感冒" in English would be " Hong Hong flu" (subject+n) you need to add a verb between the two nouns, the simplest one is "有"(has); If you treat 感冒 as a verb, then you don't need to add another verb.



  我們會回來，當時她是健康的。


Unlike in English, Chinese sentences usually state the time first, therefore, this sentence should has been "當時她是健康的, 我們會回來。"  but "當時" is a common term for " at that time (in the past)". The correct structure is 
 [ (當) + (relative phrase) + (時)] / [ (當)+(她健康) +(時)] 

當她健康時 ( when she is healthy) would be grammatically correct.

我們會回來 means " we will be back" ,  you should add the reason " to see you"  and write " 我們會回來看你" 

*You can further improve the writing by replace " 當她健康時" (when she s health) with " 等她康復後" (wait until she has recovered)

*Using terms like "尊鑒, 謹此" is too formal for someone close to you.  A casual " 親愛的" (dear) feels more intimate.

*To avoid the same subject 我們 appear twice in consecutive sentences, you can omit the second subject 我們. 

親愛的曾祖母:

我們想念你 ，
現在紅紅(有)感冒，
等她康復後，我們會回來看你，

愛你!

*is she 祖母 (grandmother) or 曾祖母 (great grandmother?)