Wow - I cannot believe some of the posts in this thread. I think everyone needs to calm down and realize that there are people on here from all parts of the world and each is entitled to their own beliefs.
Just because one person (or 20 people) believes a dog should be an equal member of the family, or should be fed only organic food, or should sleep in a bed, or should be wearing little pink tutu's around the house does not mean it is the "right" way to own a dog. As long as the dog is loved and treated humanely, there is nothing "wrong" with the way the owner is keeping the dog. I'm a little shocked and dismayed at the number of you that suggested she get rid of the dog. There are already too many in the world that are abused, neglected and homeless. While many of you might not think it's the ideal picture perfect home, this dog has one, and they love him and that's good enough for me.
Oscar's mom came here because she desperately needed advice on how to deal with Oscar. Instead of judging her because she has different beliefs than some of you, how about offering advice based on her beliefs and capabilities? Just because it's not how you would care for your basset does not mean it is "wrong".
She obviously loves the dog and wants to make it work. So based on what I've read and without any judgement, here are my suggestions to Oscar's Mom:
I'm sure you've learned from the other posts that bassets are very social and food oriented dogs. I would ignore the crying, barking in the morning. When the basset has been quiet outside for 5 or 10 minutes, I would let her (I think you said the basset is a girl) inside, give her a few treats and spend a minute or two telling her good morning and giving her some affection. Hopefully within a few weeks she will associate being quiet with getting to come in and get a treat and will start quieting down.
If the nanny is up for it, allow the dog to be with her and the child as much as possible during the day. If they are outside, so is she. If they go in for a bit, try letting her go in with them. They usually just love being around people whether they are included in the activity or not. Ask the nanny to give the dog some affection during the day when she has a spare minute and try involving the nanny in the training process with clear instructions on what the dog is allowed and isn't allowed to do and how to correct any unwanted behavior.
I think hiring a neighbor kid to take her for occasional walks and the beagle play dates sound like an excellent idea and should help her get some exercise.
When do you feed your dog? You mentioned that her food bowl is outside. Is there always food in it for her to eat whenever she wants to or do you feed her at a certain time of day. If you need her to be outside while you are having dinner, I would feed her at the same time. When you are ready to eat, tell her it's dinner time, take her out and feed her, then come back in and enjoy your dinner. If there is always food in the bowl, there is no incentive for her to go out and behave for a bit while you eat.
When you are ready for her to go out a night, tell her it's bedtime and give her a few treats after she walks outside. Try not to be overly affectionate at this time as she will just want more attention. Try putting up her toys at night so she can't play with them and put them back out in the morning.
Try to be consistent in establishing a routine for her to follow and she will probably respond to it in time. She's still a puppy with lots of energy and will calm down with age. But that might be awhile. If you are still having these problems after establishing a consistent routine, hiring a trainer to come to the house and help might be a good idea.
I think some of the posts on here had some good advice for you and I hope your situation improves before the new addition arrives.