I understand the respect part......I am a father of four young boys who has had this issue with heelys as well. The biggest issue is not only the respect you want your children to learn it is also a safety issue. It is highly recommended that a child not skate in the home for a few different reasons.
The most important is safety. Your kids may be the best skaters in the world, but children will be children and they can get hurt. A turn made to sharp could throw them into the TV, wall, or a sharp area of the furniture which could cause some serious injury's to your kids. If they are allowed to free roam with the skates on should they fly into the kitchen they could be looking at burns, cuts or injury's from the appliances. Not to mention that they could run into each other or you and dad. Safety should always be the top concern in the home.
The respect issue is also important. You want to raise your kids to be respectful of the home as well as the things in it. There is a time and place for everything.....but running or skating rampart though ones home is never the time or the place. Would you want them to do this in someone else home? I would say the answer is no....respect starts at home. If you do not teach them to respect their own home they will never respect anyone else's. There is also the issue that you and dad have things going on....a child skating though the house makes it harder to take care of your own things without having to worry about watching out for a child flying by on skates.
Now the skid marks is a disater......and reason enough that this should not take place. The reality is they are damaging the home and not being required to clean it up. This as well teaches no respect. Someone has to clean it up.....maybe that is you or dad. Or maybe you have to hire someone to come clean it up. Either way this is time lost as well as money lost due to them not respecting the home and your rules.
Since there is a area for them to skate in I see no reason why they should be in the home skating. I will admit that sometimes as parents we are too strict....but in the end it is our jobs as parents to see that our children grow up well rounded and respectful. If we fail to do so over wanting the child to have every right under the sun then we as parents have failed them. Teaching respect and understanding is the most important job we do as parents.
As for the number (3) They don't clean up after themselves very well at all---but that's our fault. We need to get on them more. Chores and cleaning up after ones self is the easiest way to teach your children respect and responsibility. Sometimes it is good for the children to be a active part of the household....a simple everyone pulls their weight theory. By having them clean up after themselves or do chores they are a part of keeping the family in running order. Instead of just being the kids who get to have fun. A good balanced mixture of responsibilty and respect is what helps a child grow into a product adult.