"detect opportunely" vs "opportunely detect"?

In the next phrase:

Only a few doctors assess their patients about the type and frequency of the tests they should be doing to detect opportunely and prevent such diseases, but we will help you solve this problem.

What makes more sense "detect opportunely" or "opportunely detect" and why? Is there a rule?

I would strongly recommend against putting "opportunely" or any other adverb inside that clause.

Only a few doctors assess their patients about the type and frequency of the tests they should be doing to detect and prevent such diseases, but we will help you solve this problem.

(As to the rule itself, writers disagree, but in general both orders are possible. See split infinitive.)

You didn't ask about the sentence in general, but it could definitely be shorter and clearer. Ralph M. has one good suggestion. Here's mine, a bit closer to the original:

Too few doctors assess the type and frequency of tests needed to detect and prevent such diseases, but we will help you solve this problem.