Welcome to drop shipping!
Where there are some big and enticing advantages to using drop shipping as a selling platform, there are some seriously big draw backs, and you've just found one.
101 is spot on, unless you are using a drop shipper that is providing tracking for you then you are always going to find yourself sitting out on the branch alone.
If it's not feasible to use their tracking option for cost, then it's pretty much a numbers game. How many sales are getting through to how many you are having problems with, and then having to cover yourself.
Not the best way in the world to run a business, but if you still have your head a long way in front, then you just have to make sure you manage the times the delivery does go south well, or they will hurt you on the feedback.
Truth is if most customers knew that they were buying of people who were buying from a second party to supply them, they would not do business in the first place.
It's one of the reasons that sellers who use those generic product images for their marketing tend to struggle. Over the years most buyers have gotten a little smart, and have learnt that these types of listings are drop shipping listings, and they will give them a wide birth.
Of course most will still end up buying from a drop shipper, they will just be a smarter one who has hidden their true identity well, but that's another topic lol
Since you do carry some stock on some products, have you considered bring in some stock of the drop shippers products so you are in control of despatch yourself.
You should always at least offer the customer a tracking option for their delivery. It doesn't have to be set as your standard option, but give them the ability to take out priority shipping and you may find some taking the option and then taking the pressure of you.