
How old was Belle when she joined your family? Anything that she experienced up to and including the first 8 weeks of her life could explain some of her behaviour.
Taking her to the vet for a physiological exam is a wonderful idea.
You don't necessarily have to pay for professional dog training if you are willing to spend a lot of time retraining her. At this point, Belle views herself as the alpha member of the family and that misconception needs to be changed.
Buy a six-foot cotton lead and a metal choke chain collar that is exactly 2 inches longer than the measurement of Belle's neck. Make sure that you put in on the right way. It should go on Belle like a letter P.
Start with the command "come" in a firm voice as you slap your left thigh. Don't repeat it. Belle's not deaf. If she doesn't come, yank the lead firmly and the collar should snap. It's not mean. Say, "Nooo". Use the lead to bring her to you. When she comes, lean down and pat her side. Don't pat her head. Repeat this for ten minutes and then play with her using a squeaky toy or ball. If you're outside, do not let her off of the lead. You can let her run around you while you make sure that you don't get tangled.
Then, as the alpha person in your family, work on the command "down". Firmly say down. If she doesn't heed the command, do not repeat it. Step on the lead so that her head goes down and the body will follow. Say, "Good girl". Practice this for 10 more minutes and then it's playtime again, perhaps with a biscuit as a reward.
Belle should always be taken out on a lead with you going out of the door first. Feed her after you eat with no begging at the table. Even looking at your food is considered begging.
If you look online, you'll find a myriad of information about dog training. Don't think of the techniques as being mean. You're trying to help socialize Belle. Like children, all dogs will test their limits to feel secure. Training her to see you as the alpha member of the family will mean the difference between keeping her or not.
Suzy
P.S.- Never hit Belle.
P.P.S.- Let us know what happens. We care!