OK. Don't hesitate to ask me about "how to do".
Let's step by step.
Create one map. Create placemarks, connected to this map. Add attributes (groups, categories, etc) to placemarks. Show map by component (menu item), or by module (just select this map), or by plugin call my map ID.
You'll get you first map correctly.
Create the second map. Show it by module/component. If you want to use plugin - I can explain later. You'll get the second map without any map objects. One note - you can't display 2 modules on the same page. You can show more than one map on the same page only by plugin.
Lets come to module. If your second map is displayed, lets add your placemarks to it. In module options you can add IDs of placemarks, and/or IDs of groups, and/or IDs of categories... All options work by AND, ie if you enter categories IDs and groups IDs, you'll get placemarks belonging to both of it.
You should create only one placemark, you don't need to create the same (copy) placemark to the other map My extension has flexible way to display map objects.
As for JQuery, map initialization type and so on. By default, I use "standard" way to initialize (ie run) my extension - by onload function, ie when site page loaded - then extension will be run. And if you install some other extension, which uses the same way, it can override my call, and in this case my maps will now displayed - only empty space. Lets today skip working on that. Try to create two maps and call it by modules. And if you can't get the second map show - give me link to it and I'll check it.
In any case, if you will have troubles - you can give me temporary access (mail me This email address is being protected from spambots. You need JavaScript enabled to view it. ) to your admin panel, and describe where you want to show maps, and I can check and fix your problem and show what I did.