1. Read something easier.
Legal writing is among the most difficult, confusing, and often painfully ambiguous writing in English.
In English, there is a well-known proverb: "You have to crawl before you can walk, and you have to walk before you can run." Translated into a maxim for learning a skill, that would be: "Crawl before you walk, walk before you run."
Unfortunately, I don't know of some easy writing that's filled with sequences of negatives that I could recommend. Maybe someone else can recommend something. But see below for a possible gold mine of easier but appropriate reading.
2. Write examples yourself.
Think of thoughts that include multiple negations, and experiment with how to express these clearly. One of the best ways to learn how to understand language is to express yourself in it. Then you can empathize with the authors of complex writing. You can see how they, too, struggle with making complex negations clear—and you can better tease out the meaning they're trying to get across through the many resources of English grammar.
3. Re-state hard examples in your own words.
I think you've already been doing this; it's a good idea. Rewriting gives you great command of the options that English has available for expressing complex ideas, and mastering the subtler shades of meaning and emphasis.
Talking is of course the most important part of mastering a language. It sounds like you're only having trouble with the kinds of complex thoughts that occur mainly in written sentences, not spoken ones. But explaining a complex written sentence out loud, to a live person you're trying to get the idea across to, is still extremely effective. Usually you end up breaking the complex idea into smaller sentences. This is good. It forces you to slow down, empathize with your listener, and notice exactly what each negation modifies.
As a less-difficult source of complex negations, you might try reading something in a moderately technical topic—say, gardening. Hitting Google Books just now, I found Gardening Indoors by George F. Van Patten. Here are two examples of multiple negation that I found searching for the words "not" and "unless":
The horticulturist is able to wield control over many factors influencing growth. Since few people have ever played Mother Nature before, they usually do not fathom the scope of the job.
Rewriting the second sentence to be super-clear, breaking it into two sentences:
The number of people with experience playing Mother Nature is small. So, most people don't know how big a job it is.
Unless fortified with nutrients, soilless mixes contain no nutrients and are pH-balanced near 6.0–7.0.
If a mix does not contain soil, then it does not contain nutrients (because soil is where nutrients are normally found). But a mix without soil could contain nutrients if the mix were fortified with nutrients.
Of course, it's best if the moderately technical topic you choose is one that you're interested in learning about anyway. Then you'll be learning the topic through English. Communicating through English should be the main way that you learn, supplemented by a relatively small amount of talking about English.