Your description of the situation doesn't sound quite as bad as your first post seemed.
Do continue with your socialization of her, keeping an eye on her so you can pick up on her first signs of discomfort. Ideally, you want to expose her to as many new places, situations and people as you can without going over her comfort level. Let her go at her own pace when she is exploring new things. The classes you are in should help her too...she can be introduced to dogs and strangers, but in a controlled situation so she can back off when she needs to.
Her peeing when she is approached by your husband is a sign of submission and discomfort. There are some ways to help her with that. This article, for example, gives a few hints on how to deal with it. https://www.humanesociety.org/resour...tion-solutions
I wouldn't take your neighbor up on getting your two dogs together until you really know your pup and have a good handle on her behavior. Even then it wouldn't necessarily be a good idea. Dobes as adults aren't really that interested in other dogs anyway, and the last thing you want is for her to mess up again with the neighbor's dog.
Of course, keep her on a leash when you are out and about, keep up your vigilance when you are near kids and other strangers, and be extra careful to make sure she won't get out of your yard again. If your kids have friends over, you should keep her on a leash with you in direct control. By all means expose her to the kids; don't lock her away, but she shouldn't allowed to be in the middle of things. Work on those puppy manners; that will make a huge difference in your lives together.
I hear you about the money (we've been the vet route too) but shouldn't be terribly horribly expensive to bring someone in for a one-time evaluation who can see her in her everyday environment and give you some specific pointers about what you should and should not be doing. Make it clear exactly what your concerns are and what you expect from the behaviorist, and see if you can find someone who will come in for a one-time visit. It would probably be worth it for you to explore that option.
Do avoid going to anyone who suggests any kind of negative or punitive action to work with her problems. At this point, that is not what she needs from you and would in all likelihood make her behavior much worse.
You now know a little more about how she will react when she's under a bit of pressure and unsure of her environment. It's up to you to help her gain confidence and achieve some balance.