Legalese

Could you just paraphrase (in a simple, easy-to-understand manner) the following sentence quoted from a statute?

I’d appreciate at least two responses - one from a native and the other from a non-native user. Thank you.

My try:
Every rule …as soon as it is made, shall be laid before each [of two Parties involved] House of Parliament during their corresponding sessions (no matter, one or more, but within a 30-day period of time).
Should both Houses make any modification… and agree on it before the expiry of the session immediately following the one making the Act valid, the rule or regulation shall thereafter have effect only in such modified form or be of no effect… Any such modification or annulment shouldn’t contradict validity of anything previously done under that rule or regulation.

Thank you, Eugene. But did you modify it? Now it appears to be more comprehensible with ‘no effect’ and ‘previously done’ simplified.

Yes, having read the last sentence, I found I’d misread the final part of the original and tweaked it.

I wish I had other responses, too. This was a test given to a group of Law students. They were directed to simplify the sentence in as many short sentences as they might like without any distortion of the points involved.