I've had no experience with mosquitos since I live in Ireland but is there any chance you could get a mosquito net and put it around there living space?
I have a fly strike spray that I spray on the rabbits and their living space everyweek. It works for mosquitos too (says on back of bottle). It repels the flys COMPLETELY - I havent seen a fly near their hutch in ages lol! Maybe you could get something like a mosquito spray or something
Heres the one I use: https://www.thehayexperts.co.uk/Heal...ector.513.html
Its so cheap in the UK lol