Can you do a short term foster of a dog from an animal shelter? One that needs a home while waiting for its forever home. We have high euthanasia rates in some shelters here (US) so a lot of times dogs are fostered while forever families are sought. This would give DP time to fall in love with/not fall in love with a dog with it not being permanent.
Get a Chiweenie. It's a cross between a Dachshund and a Chihuahua. My teenage daughter has one. It's tiny and she has trained it to use puppy pads when in the house, is extremely cuddly and protective. She snuggles with my daughter and growls at me if I come in the room to wake her up. If I play hit my DD on the leg or arm, the chiweenie will grab my hand in her mouth but not hard. Loves toys and chew bones. Very very smart and learns quickly. While it does shed, its fur is very short so is not as noticeable as a bigger dog. She stands her ground against the much bigger dogs in the house. I highly recommend them! Some have floppy ears, some have pointed ears. I prefer the ones with floppy ears myself.
For what its worth, we had a dachshund growing up and never had any problems with potty training. She lived to be 18+ and didn't have back problems until near the end.
Chinese pugs - those are impossible difficult to potty train and need attention from the vets when their anal glands get infected. And their bug eyes water and get goopy from allergies. One of the two we have has skin allergies, the other occasionally has an allergic reaction to something that makes his face/nose swell and have a hard time breathing. For as small as they are and as short as their fur is - they shed a LOT.
Rat terriers - those are very loyal dogs and very very good with little kids. My daughter's is potty trained. He also is content to lay around during the day without stimulation while we are away from home. He defers to the Chiweenie as if ladies and little dogs first. He sheds more than the chiweenie but much less than the pugs
Yellow labradors- My parents have one that comes to stay with us sometimes. The tail hits on everything - no one can sleep through that. And rain - The whole house shakes from her shaking in fear - she's our weatherman. Loves loves loves water that is not falling from the sky though. But very loyal. And very good with kids. Sheds a lot. Needs a lot of walking / stimulation
Rottweilers - Hard to know what to say about them as we have only had ours for a half a year after getting her from the shelter. Our previous rottweiler was older when we got her and quite overweight. She was lazy lazy lazy. This one has a bunch more energy. She chases the horses next door and has to stay on a chain when outside so she doesn't run the horses into a fence. Sheds a lot. And she is big enough to steal things off the kitchen cabinets 
. Neither the previous one or this one likes other dogs to fight and barges in to them growling trying to break them up. Needs a lot of walking / stimulation.
We have another dog, but I don't know what kind she is as she was a stray that we found and took in. She is a mix of some kind.