Lynette,
yes, Yes, YES. I think it would be abnormal if you didn't feel some separation anxiety. When I divorced my ex, the girls were 1 and 3 yrs old. Whenever they went to their dad's to visit, I worried. And I always prayed that nothing would happen to them on his watch, because I knew I would blame him big time, even if it wasn't his fault.
You are dealing with some tough stuff in your life right now. Plus you are separated from one son, and now temporarily from a second one. And then the cat goes and dies. It is a downer for someone without bipolar. However, when you are bipolar and life tanks around you, it's tougher. Do you have a good enough relationship with your doctor to call and let him/her know that you need some help? If you are dealing with depression, I am guessing that you either stopped taking your medication, or your meds aren't working for you right now. If it is the latter, call your doctor and maybe the doctor can adjust your meds so you feel less depressed. Missing your kids isn't easy, but it shouldn't spawn an outright depression. Crying is okay, and feeling sad is okay, but if you feel you are spiralling down to an outright depression, you really need to get some help from the medical field. It's not uncommon to need to change your meds from time to time, and the stressors in your life right now could be good reasons to do so.
Other things you can do, in addition to checking with your doctor about your meds, is to plan some fun things to do with the kids you have at home. That's what I do when my husband goes away on business trips. I tell the girls Daddy will be gone, and we dream up activities we can do together to make it a "girls" weekend or something like that. he was away last weekend, and (they are teens) we went to a football game together, then we went to the high school band competition. Of course, they are bigger, so they found friends and ran off, and I went alone, but I expected that at the football game, and I volunteered to work the band competition, so I was in the concession stand and was busy all night, while they hung with their buds. But we all kept busy while Dad was away. I don't know how old your kids are, but maybe you can come up with some things you can do together, that are special. Remember that they are missing their brothers, too. :-)
Take care and get some help. You took the first step by writing to "all the moms out there" to get a reality check; and you should probably follow up with a medical reality check so you know you have the medical support you need to stay on top of the bipolar thing. While it's a pain in the butt to take pills every day, it's better to take pills than it is to go through depressions. I'm proud of you for sharing. You are doing it right.