My store's shipping rates are incredibly high. I use UPS, and even UPS Ground is often more expensive than the items being ordered. Customers have called to ask for discounts because our rates are way too high! We drop ship and use Quantum View for tracking. I have Shopify set to use the XML key from our UPS account.
If you're dropshipping, see if you can ship on your suppliers account instead, because of volume their shipping rates will always be cheaper.
To get heavy discounted rates, you can use Shopify's UPS rates. To enable that, just hop in to Settings --> Shipping --> select your zone -->click on calculated rates and you can select default UPS from Shopify. These rates are discounted as Shopify as an existing contract with UPS. However, if you have your own UPS account and are looking to get discounted rates, then ideally you have to contribute volume to UPS. Once UPS understands that you are giving them more and more orders on a daily basis, they will be able to renegotiate your contract. You can try the Multi carrier shipping label app to show these discounted rates to customers at checkout, and tracking can be performed from within the app. So no need to go for separate solutions for different functionalities.