For Logan I'd suggest you buy a long line (old fashioned soft clothes line) and tie it securely to Logan's lead. Until your OH is better, just exercise Logan on the line, he can run around quite easily and it won't do him any harm. When OH is better you can see if Logan responds to him off lead or if he just gives your OH the run around too. If its the run around, then you'll have to teach recall on the line so you can haul him in when he ignores the command or whistle.

For the puppy, you have to have a firm and positive attitute - don't comfort her as she really will think there is something to be frighened of. I's suggest that you go and sit on a bench somewhere people will pass by but not to busy a place. As someone approaches, give her a little treat and say Good girl so she starts to associate something pleasant (treat) with someone going past. On the lead, as you walk down the street have her by the wall so you are restricting her options for hiding and just keep going, you'll probably be pulling her at times so just very short walks as you don't want to stress her joints, and you will have to pull a bit. For stationary cars, have her on the car side, you by the wall and walk her briskly past them - as she improves, decrease the space between her and the car so eventually she can be by the kerb. For the last walk at night, for her safety keep her on the lead - letting her off lead to go dashing home is just building up issues for the future.
She sounds like a sensitive pup and you'll need to be careful in your handling of her - lots of praise when she is coping and build up her confidence. I'd also suggest that you take the pup out on her own to build up the bond with you without you being distracted by Logan. Also, you don't want her picking up Logan's bad habits

As for the little presents Logan is leaving for her, take the pup out first to go and pick up after her, then Logan and pick up. Start to teach her a Leave it command and use it when she goes near any poo, anywhere. Sometimes she will just get it before you see it, well tomorrow is another day. There is a chemical method sometimes used effectively on dogs eating their own poo but I would not use it for a young pup.

Hope your OH gets well soon and you don't catch his flu!

Sgurr