Corona vaccine is never really necessary. They may get it but it is usually no worse than a three day cold. Ellie's vet gives it also and I wish I would've known before that it isn't right. With vaccine protocols you really have to take control. There are so many side effects with them that over doing is not something I would want to do. I do understand your dilemma though. It is hard to talk to a vet about it because "they know everything". You need to find a vet you really like and that will listen to you.
Is your area having a lepto problem? Lots of vets like to give this vaccine but it should NOT be given if there isn't a really good reason. With the risk of it killing Yorkies, it isn't a good thing to give. Reactions get progressively worse with this shot.
Corona isn't necessary and definately not after 8-10 weeks.
Lyme's vaccine could cause kidney damage. Yorkies have problems with this anyway. It is too risky and Lyme's is usually very treatable if caught in time. I have never seen a vet set on as many vaccines as your.
Maybe print out some info from AVMA or AAHA on their protocols and take it to your vet?