It sounds like your cocker needs some professional help, I'm afraid - a behaviourist who is experienced with Cocker Spaniels will be able to observe the issues far better than we can over a forum. Steer clear of any behaviourist who makes any comment about her colour...
I will give some comments in the meantime, though...
Re: Seperation Anxiety - this is quite a common problem. What happens when you leave her? Does she have a crate or other den to go in? It's not unusual for dogs to experience SA even with other dogs present, as it is the human company they crave. It can help some dogs to set up a regular routine for when you go out so they know what to expect, though for some this can make things worse as they start to worry before you go. I always leave the radio on for Honey, leave her with her special toy and a kong stuffed with something yummy... she gets really excited when she see me getting ready to go out, as she knows she gets good stuff!!!
If preparing to go out makes your dog anxious, do the going out routine several times without going out, until she stops being anxious about it, before you even begin to address the going out. Once you can do that, you need to build up leaving her from literally a milli-second up to longer periods of time, going at HER pace, never letting her get to the point where she is anxious - it's a long process, and if you have to leave her at any point to the point of distress it can undo a lot of progress.... but it is acheivable.
Re: Jumping up to things on the side - the simple answer is don't leave anything on the side to tempt her - dogs are scavengers by nature, and once she has learned that there might be tasty morsels on the side she's going to keep checking it out. Restrict her access to the kitchen when there are things on the side - if it isn't rewarded (by her getting food) the behaviour will decrease. You can also train an "off" commmand, so that you can ask her to get down from the sides if you catch her up there (say off, and throw a treat down on the floor so she follows it - but I would do that from something other than the sides she scavenges from, as she could be clever enough to learn that she gets rewarded for jumping up!!! - once she has learned it elsewhere you can apply it to the side she scavenges from!).
Re: Being in Control - I'm not sure what you mean by this, nor what you mean by trying to "bring her in line". But from everything you say, it sounds like you have a very nervous dog, she's not trying to dominate you or rule the roost, she is trying to keep herself safe from the threats she perceives in everything around her. I expect (though I'm willing to be told otherwise) that the times she has gone for you are times when a confrontation of some kind has arisen (maybe she's got hold of something she shouldn't have and you've taken it from her, or you've been trying to put her lead on, or groom her, or remove her from somewhere??). It is far better to adopt a more positive approach to training - dogs will repeat behaviour they find rewarding, so reward everything she does that you approve of (including lying calmly and not doing anything!), distract from behaviour you don't want (so that it doesn't get the chance of becoming rewarding) or if that's not possible ignore it (for some dogs even negative attention is rewarding). The most I would do to "punish" a dog (especially in this kind of situation) would be to remove my attention by getting up and walking away. If you give us some specific examples of her behaviour, we might be able to give you some more insight.
Re: Barking at strangers - this is a fear reaction - try not to let her get to the point she is scared by calling her to you before she reacts to the person, and giving her a treat. If you can set up stooge people to walk past her (at a distance she finds safe) and, intially, you treat her as they walk past - as she gets more confidence, you can progress to the stooge throwing a treat towards her (but don't let them have eye contact at this point) and gradually to being closer, and then taking a treat from the person (in her time - don't rush it - and don't introduce eye contact, or any movement from the person to her until she intiates it). I have helped a chap with his nervous collie by doing this, and she is much improved, but it is has taken time and patience.
You should also get her checked at the vets, just to rule out any medical reason for her behaviour.
In general I would advise handfeeding her her food for the time being - use half of it for rewards for all the things I've mentioned above, and the other half just sit and handfeed her. She sounds like a very scared little dog and this can help create a positive bond between owner and dog.
If you do decide you can't manage her issues in your situation, please contact a reputable rescue organisation, as they will be able to find the perfect home to help her grow into a confident happy adult dog.
I hope this helps.
