Glass is almost always part of "comprehensive" or "other than collision" coverage. (wording varies by company). Some companies offer a separate "glass coverage" or "deductible buyback". Most companies offer to waive the deductible if the window can be repaired rather than replaced. The situation you have is not uncommon, it is actually the norm.

As long as your policy carries liability for injuries to others, property damage for damage to other property and collision for damage to the rental vehicle you should be fine. That is unless your policy excludes rentals. Most policies don't but some companies won't extend to rentals. Comprehensive will cover fire,theft and generally glass, flying objects etc. You will have to pay your deductible and yes, if the accident was your fault you could possible lose a driving discount but that all depends on your state and your insurance company.

Sorry that you've had this hassle to cope with, apart from the expense. Around here, we have no fault insurance. When I was in an accident and not judged at fault, my insurance paid for the write-off of my old car ('93 Ford Taurus). Paid me about what I'd bought it for, about 6 mos. previously. When I (evidently) ran the red light, as I was found to be at fault and ticketed, there was no compensation ... I had to suffer the loss of my car. Actually, I fixed it, at larger cost than it had cost me to buy it, about 6 mos. earlier, as it appeared, at about 120,000 mi., to have potentially quite a few good miles left in it and it seemed a waste to scrap it, though it was close to 20 years old. It costs a great deal of precious energy, plus adds to not only pollution but to global warming as well to build a new car for me (or the portion of its life that I'd use in an older model). Even if she had insurance, if she had no driver's licence, they likely would not have covered, in any event. The owner of the car had responsibility to ensure that only licensed drivers drove it - apart from it being stolen. When my friend the milk man wanted to go on holiday, with his son to drive the route, son had to upgrade driver's licence from, supposedly, permission to drive truck to one with air brakes. There was ice in the home when I visited, as it appeared that the son had only licence to drive a car, the Dad had given him the devil, the Mom was angry at Dad for hurting her son's feelings ... and found it hard to get her head around the fact that every time the son drove that truck out the lane unaccompanied by a properly licensed driver, he put at risk everything that they owned ... as the insurance company would not have covered any trouble. Actually ... I upgraded my truck licence to coverage for air brake and rode around sitting beside the son as he did the driving, or I drove the truck myself. ole joyful

Keep shopping then. Most preferred companies allow up to 5 days with no prior insurance. Is the surcharge with you for the first term or will it continue and for how long? I always encourage my new business to wait to cancel until they have my policy and are pleased. There is never any reason to jump on a cancellation of a policy until you have proof you are covered elsewhere. Binders are not necessarily what you will want either. A binder shows proof of coverage but the underwriting isn't complete and rates could change. Policy on the other hand is complete for that term. A policy cancellation can be backdated, a good insurance company will generally ask for proof you are covered.