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