First question, and this is very important, Was this natural or a c-section delivery? If natural you can follow the advice I give now. If it was a c-section, you need to wait 4 more weeks before doing anything.
Your doctor is absolutely right. Doing typical exercises will make your problem MUCH worse. Do NOT do any standard exercises right now.
Abdominal separation is when the left and right side of the rectus abdominis become separated from the uterus pushing out. The rectus and the obliques control all your abdominal movement. Then there is the transverse abdominis Which really just holds your guts in. This internal abdominal wall is what you need to strengthen first! This is what will flatten your belly out. Working the other ab muscles will just pull it out more.
The exercise you want to do is called a stomach vacuum. Sit up straight exhale all your up let your chest expand and suck in your stomach as much as you can. Visualize your belly button going all the way back to your spine. Hold it for 20 seconds. Then breath for a minute and do it again. Start with 3 sets of 20 seconds every day the first week and just slowly work your way up to 5 sets of 40 seconds or however long you can comfortabley hold your breath.
I want you to do that for at least 3 if not 4 weeks before doing anything else. Even after that time do at least 3 sets every other day or so.
After 3 or 4 weeks of only vacuums, start doing something that works the abs indirectly by making them contract, but not actually move.
First do your arm and shoulder exercises standing, maybe even do 1 arm at a time. Try doing some body weight squats, just body weight, do not add any weight to these yet. Concentrate on keeping your stomach in and tight, don't let it hang out. Then do a kneeling stability ball roll out. Here is a link on how to do that.
You also want to walk with good posture, don't let your gut hang out. These exercises will get your lower back a bit too. Just don't do anything that involves bending at the waist and hips yet.
After 4 or maybe even 6 more weeks just to be on the safe side, you should be able to do deadlift variations, add weight to squats and do weighted situps and all that stuff just like before.
As for cardio, the first or 4 weeks while you are doing vacuums, you should stick with walking or maybe light swimming. after that anything goes within reason.
Also remember your nutritional needs are still going to be pretty high if your baby is going to be getting only breast milk for a while. I would think loosing weight real slow and not doing anything crazy with your diet would be best.
Here is a link to site I got from a search that has a test for abdominal separation, but irregardless of results, work the transverse abdominis first.
Hope that helps. Let me know if you have any questions.