Timid at home, boisterous out and about?

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Hi There,

I've owned all kinds of dogs all my life but have never come across what my little girl suffers now.

She is 3 years old now and we've had her since she was a tiny puppy. We also have 2 cats and a labrador/pointer x (Geroge). We had the other dog before we got little Olivia.

She is scared of everything at home and lives under the sofa only to come out to eat or to go for a walk. She rarely eats but that's because she walks away from her food and lets George eat it.

I try to train them both for a few minutes every evening, basic things like sit, stay, down etc. George is perfectly obedient, she will run into the kitchen (she can hear the treat tin being opened) realise what's happening and wait. When I try to give her a treat she does nervous pee, tail between legs and runs under the sofa.

The nervous pee and running away is also standard when anyone says hello to her or tries to excitedly play with her.

She doesn't like to go out into the garden (the standard first/last thing of the day for peepee)

She even ran home about 0.5 mile (over a main road) because my stepson and nephew took them for a walk and she decided she didn't want to be out with them. As soon as she was off the lead she came running home to me.

I don't know what to do. She's never been badly treated, George is a dominant and jealous boy but we try to share equally between them. The cats adore her and she actually plays with them happily. I really can't understand where I've gone wrong.

Please help.