If a broker has accepted a vehicle for cover then that cover must be good - so long as you do not violate any of the conditions or make any false statements as to the identity of the vehicle. Any failure of cover would be down to a failure of the arrangement between broker and insurance provider - which is not within your control, therefore the broker would be liable for any claim you may have to make.
If your is U.S. and they have not specifically stated that U.S. vehicles are not covered or have not asked you if it is U.S. then they will be liable as you have no control over their agreement with the provider.
It is normal practice for insurance providers to continue to renew existing arrangements but decline new business if they wish to limit their exposure to a particular market - also to jack up premiums on existing business if they want to get out of a specific market. Their choice, not yours. The broker can only offer what is available to them
But you are the customer - if your provider does not want your business you have to find another provider through another broker who does. Now that IS your choice! :-D Then again may simply be the broker who is jacking up costs - there is no way you will know, but you have to shop around. Isn't this begining to sound remarakbly like the domestic electricity / gas supply market?
One interesting point - and I don't know if this is correct: I wanted cover through a particular provider, not too concerned through which broker as had no bad broker experience to date that I wished to avoid. I had previously left this provider and gone with another broker and new provider - as before (causing the first move) the broker then increased premiums to an uncompetitive level (this might have been due to the provider upping cost of cover, not the broker's fault). When I asked a couple of brokers if they dealt with my preferred provider, I was informed by one that they could not quote for business if I was already covered by that provider through another broker, but if my cover was not currently with that provider they could certainly do so. Which suggests that should your broker jack up the cost you may be forced to jump ship to another broker / provider for a year and then seek new quotes with your preferred provider. Hey ho.