What type of hay do you use? If it is Timothy you can switch to a different type of hay to help with the allergies. I had to switch I was becoming developing asthma. Now I still use timothy but its 3rd cut so its all leafy. Its the only thing that helped but some people use orchard or meadow grass hays. That’s something you might try.
I think what stormyRabbits suggested above is good. Also when it comes to the baseboard issue you can try to wipe something on the baseboards like vinegar or what I have used is mild hot sauce. You want to go lightly with it. Things like that deter the chewing in some rabbits. The hot sauce was the only thing that stopped mine.
If your parents really want to put them in a pet store type cage you can get 2 of the largest size cages and combine them. One small pet store cage wont work for one bunny much less two.
As far as the odor in your cage what do you use in your litter boxes? I use carefresh and I clean my little boxes every other day. I put the bedding in then hay on top and the next day I top with fresh hay. I use to change their boxes daily. Remember to give them a good cleaning with a little water and vinegar at least once a week that also helps with the odor.
Oh and how long have your rabbits been bonded? Mine have been recently bonded and we are having poop wars as well but they are getting less and less every week. I just clean them up when I see them.At first they were really smelly.
I hope you and your family can come to some agreement that is beneficial to your rabbits and the whole family.