Hi Amy

There are quite a few LR peeps in Texas, hopefully some of them will chime in on dealer or indy not too far that you can get it serviced.
Taking your LR3 to Jiffy Lube is asking for trouble IMO. My advice to you if you plan to keep it, is to start learning up on how it works, or you may become a prime victim for asshats to rip you off. The forums are a very helpful, for LR3's in particular,
DISCO3.CO.UK - Dedicated to Discovery 3 and LR3 Owners and Enthusiasts is a great technical resource. You can change your own oil and basic maintenance stuff - you don't need muscles and it's pretty easy to do.
Clogged sunroof drain is likely the cause of your leak. Here's a DIY for it
DISCO3.CO.UK - View topic - How to fix a Sunroof Leak! Not sure about your remote, possible there could be some wire corrosion from the leak or something.