How to cut a group out of another group - or flatten?

[edee]

I’ve been working on this for 3 days, can I get a hint, please. 
I’m not looking for a step by step. If you can just give me the right words for what I need to do, I’ll start Googling again. 

How do I do this? (Please see attached image )
(In PS speak) What I need to do is flatten the black raindrop group and the white background group, then cut out the black raindrops so there are just holes where the black raindrops were. Then I need the white rectangle, the white donut and the white background to be flattened and then stroked. 

NOTE: The blue background is just so you can see the white. 

Here’s how I made it: 

Black raid drop things are in a group, no stroke
The white background: I took the black raindrops group and duplicated it, then gave the duplicated raindrop group a white 5.2 stroke. 
The black raindrops are laying on top of the stroked raindrops. 
Rectangle has a 5.2 Stroke, no fill
Donut no stroke, white fill, but it’s a donut.

I can do this in PSE6 (10 year old software), but I can't figure out how to do it in AD. And I REALLY want to get away from Photoshop and Just use AD.

How can I make the AD image look like the image I made with PS? 

Thank you. 

 

[toltec]

It would be so much easier if you posted the file.

If it is a pixel file, you could do this in about 5 seconds but unless the resolution is very high to start with, it will be a bit rough (pixellated) around the edges.

Just select the white and put an outline around the selection outline

It would be much easier (probably) and certainly better if you started with a vector file.

[edee]

I can post the file? That has been against the rules in so many forums. Heck yes! 

It is 300dpi - I'm thinking that's large. I tried doing something called Rasterize, but that made it all pixely.

Heart Box 2.afdesign

[edee]

I Got It!! Only took 3 days, but hey, I'll never forget it. 

Thank you!

[JimmyJack]

2 hours ago, toltec said:

It would be so much easier if you posted the file.

If it is a pixel file, you could do this in about 5 seconds

 

And in Vectors it'll take about 50 seconds 

@edee you can't add or subtract grouped items. So you have to combine similar items together (and expand stroked items) into curves objects first.

(edit: whoops, missed ya by 1 minute. Glad you got it. I'll leave this up in case it'll help others.)

[edee]

Well, darn! That is much easier than what I went through. I practically redesigned the entire thing. 

Thank you. I'm going to go back to the original file and try that. 

Thank you so much!