I am going to have to echo Erin's comments. I know from personal experience what it's like to lose sleep because your yorkie has to get up to go pee, every single night of the week!
Millie has always gone in the middle of the night. In the beginning she did it 2 x a night and now she is down to 1 x a night. She is 3 years old! I know she will have to go in the middle of the night for the rest of her life. I am ok with that. It first started out as whining from her crate, then when she was reliably housebroken, we let her sleep with us and now she climbs on my back and chirps in my ears and will keep at it until I wake up. (sometimes, it takes a while for it to sink in thru my heavy sleep daze
) So for her to get me up in the middle of the night only reinforces to me that she is housebroken! She will not do it in the house. So I rejoice at this!!
So be thankful that your yorkie whines to get you up to let him out. I think this is splendid and should be looked at like a "positive".
(I have just acquired a rescue that will not let me know she (Jazzy) has to go. She does hold it most nights throughout the night, but every now and then she will just do it in her pen and move to the side to avoid it. She will do it on her pillow where she sleeps if there is no other room to go). So you need to reward your little one for whining, because he cares enough to let you know he has to go out.
Oh by the way, I am 52 years old and I work starting at 7:30am five days a week. Having Millie 100% housebroken is worth maybe 5-10minutes of loss of sleep every night.
I too have noticed that Millie will sleep the entire night, only when we have had a
very very eventful day and she gets very little sleep during the day. These would be week-end days. Because even though she gets a good 30 minute walk every day and she is active as soon as we get home from work, this is not enough to keep her from waking up a least the 1x a night.
I hope you find the right solution for both you and Logan.