I'm sorry to hear of your pet losses 
We added a second dog to our family this past December, so it's all fresh in my mind
I had had pets all my life, but never two dogs at once, so I was a bit nervous at first too.
Our experience has turned out very well after an initial rocky adjustment. Our first dog is a Shih tzu mix, she is super laid back and always seemed to love meeting other dogs on walks, so we thought she'd like another dog in the house, plus we really wanted a second dog because we were always "fighting" over who got to cuddle with the dog lol. So when she was two years old, we adopted a Papillon mix from a rescue. We had a meet and greet too, it seemed to go ok, but it definitely took both dogs awhile to adjust. Dog 1 was less than thrilled with sharing our lap, and Dog 2 was very needy and I think nervous of being abandoned, so she wouldn't take no for an answer about sitting right on our laps, and dog 1 would growl and bare her teeth every time. Every time we'd give Dog 1 love and attention, Dog 2 would come barreling and push Dog 1 out of the way. Dog1 eventually stopped with the growling and teeth baring, but was now pretending Dog2 simply didn't exist. We followed our vet's advice by just trying to keep treating Dog1 like the alpha, giving her treats and attention first, letting her sit on our laps and trying to make Dog2 sit next to us, and so on.
It's been four months now, and things are going very well. I don't think Dog1 necessarily loves and adores Dog2, but I think she has grown to appreciate certain things. The two dogs wrestle and play together and chase each other in the yard. They both walk vey nicely together on leashes, and will even nuzzle each other's faces a bit while walking. Dog2 is just in the past couple of weeks FINALLY not trying to push Dog1 off our laps, she seems more secure now.
For our part, we are happy with adding a second dog. Our son loves both dogs, but our DDs in particular are just thrilled to have them, my 10 year old said just yesterday, "I'm so happy we have the dogs. I can't even out it into words how much I love them". That makes the extra work worth it!
Best of luck in your decision. I hope you can find another dog that gets along well with your other dog, and who also can bond with your DD

We added a second dog to our family this past December, so it's all fresh in my mind

Our experience has turned out very well after an initial rocky adjustment. Our first dog is a Shih tzu mix, she is super laid back and always seemed to love meeting other dogs on walks, so we thought she'd like another dog in the house, plus we really wanted a second dog because we were always "fighting" over who got to cuddle with the dog lol. So when she was two years old, we adopted a Papillon mix from a rescue. We had a meet and greet too, it seemed to go ok, but it definitely took both dogs awhile to adjust. Dog 1 was less than thrilled with sharing our lap, and Dog 2 was very needy and I think nervous of being abandoned, so she wouldn't take no for an answer about sitting right on our laps, and dog 1 would growl and bare her teeth every time. Every time we'd give Dog 1 love and attention, Dog 2 would come barreling and push Dog 1 out of the way. Dog1 eventually stopped with the growling and teeth baring, but was now pretending Dog2 simply didn't exist. We followed our vet's advice by just trying to keep treating Dog1 like the alpha, giving her treats and attention first, letting her sit on our laps and trying to make Dog2 sit next to us, and so on.
It's been four months now, and things are going very well. I don't think Dog1 necessarily loves and adores Dog2, but I think she has grown to appreciate certain things. The two dogs wrestle and play together and chase each other in the yard. They both walk vey nicely together on leashes, and will even nuzzle each other's faces a bit while walking. Dog2 is just in the past couple of weeks FINALLY not trying to push Dog1 off our laps, she seems more secure now.
For our part, we are happy with adding a second dog. Our son loves both dogs, but our DDs in particular are just thrilled to have them, my 10 year old said just yesterday, "I'm so happy we have the dogs. I can't even out it into words how much I love them". That makes the extra work worth it!
Best of luck in your decision. I hope you can find another dog that gets along well with your other dog, and who also can bond with your DD