Which form of this word is more appropriate for general use?
I would expect someone to misread reestablish more often than re-establish, however it is more consistent in context with renew, reconnect, and retry.
A number of dictionaries (e.g., 1, 2, 3) have entries for reestablish making it acceptable for general use. While I personally find the spelling a little jarring, I'm fairly certain that this is simply due to the fact that I do not come across this variant very often. If not, I would also find cooperation to be similarly disconcerting.
Cooperation used to be (and sometimes still is) spelt as co-operation to ensure that readers did not misread it as coop-eration. This Google Ngram confirms that cooperation is now the preferred choice. Similar cases can be made for preeminent / pre-eminent and preexisting / pre-existing. What has made this shift in preference possible is that none of these words in its unhyphenated form can be confused for some other word. An ELU answer on hyphenating compound words covers this issue well.
Therefore and returning to the case of re-establish vs. reestablish, it comes down to a question of popular usage and somehow gauging if one spelling trumps the other. On ELU, we do this by comparing Google Ngrams. The following Ngram for reestablish vs. re-establish suggests that the hyphen is steadily becoming unnecessary.
Narrowing this down further to specific corpora:
Another benchmark that can be used to gauge usage is Google Trends which examines web searches (along with other criteria). The AmE trend comparison for reestablish vs. re-establish (and reestablished vs. re-established) further confirms that the hyphen-less variants are the ones preferred.
Going by the above results, it is fine and possibly a good idea to use reestablish in AmE and stick to re-establish with BrE. The implication is that AmE readers are unlikely to be confused or otherwise put off by the spelling. When writing for a world audience, the safer and less confusing option would be re-establish.
When the prefix ends with the same vowel as the word it’s prefixing begins with, it’s common to use a hyphen to separate them.
When these letters are vowels, in older typesetting traditions, particularly those free of the typewriter’s tyranny, one used a diaeresis on the second vowel to indicate that it was in hiatus.