Does she get good play & outside time to just be a dog & develop her dog instincts with your lifestyle? If not, she may develop some behavior problems as dogs are active & fun-loving little creatures. An "only dog" needs either another pet in the home or someone to give them some doggie time & with a Yorkie, they need to be constantly supervised when outside due to their small size & huge prey drive as they are tempted to run & chase squirrels, other dogs, cats, etc. What if she should get very, very ill - are you prepared to properly vet & care for her, including the time & great deal of money it could take, through the rest of her natural life? These are all things to consider long & hard. Does she have some time with you for training and playing games if there is no other dog or child to play with her & keep her active & challenged? If not, again, you could have some problems with her. On the other hand, there are some sedentary type dogs who don't require so much attention and do well living a more solitary life. My Jilly was one of those quieter, more solitary dogs who did well on her own while I worked & didn't care much for play. She insisted on being an "only dog". My Tibbe who I have had 4 years is a fireball of energy & happily for both of us takes all of my time & I suspect he would be miserable living like Jilly lived. He would love a houseful of brother- & sister- Yorkies!
Usually the relationship a true doglover has with his or her dog is largely one of wide-eyed, besotted, head-over-heels puppylove on both sides, happily all-consuming & they are more than ready & able to accommodate the dog's needs & wishes,
loving 99.99% of it & never resenting one moment of it. If you don't feel that way and feel that your family & this girl may be happier with someone who has the time & inclination to devote more time & attention to her wants & needs, you & she may be happier if you rehome her. If you do, I would consult with someone here on how to correctly place her in a responsible, forever dogloving home of someone who will never breed her & who fits a strict bill of must-have characteristics. I think you were honest & forthright in your post & that kind of self-awareness is a good, good thing in any situation.
I hope you can work out what is going to work best for you & your family & your little Yorkie. God bless!