Both of my daughters (currently 9 and 11 YO) have shown an interest in whatever I am working on for years, and I encourage it. I have no interest in them growing up to have to rely on a guy to do everything for them, the more independent they are the better. Quite often when they see me working on something they will ask, "Can I build something?" I used to look at that as an opportunity to set them up with a few simple tool and some explanation, and let them give it a go, but that usually ended up with them having so much difficulty and frustration that an hour and a half later my wife will be out there asking why it takes me so long to patch a fence. Meanwhile both girls now have a new chair and bed for their dolls.
Instead I now usually try to get them to help me with my tasks. They both love to hold the cordless drill while I help them drive in some screws, or measure a board and draw the line, etc. It still takes me much longer than normal to do a job, but at least I get to make some progress and if they get bored halfway through I can carry on with the job instead of first having to finish off the doll chairs by myself.
I also keep an extra set of hearing and eye protection in my tool bag all of the time, so if they walk up halfway through a job I am ready for them and don't have to make a trip to the house to get the gear they need. Another task that they often help me with is painting. They love to do it and are at the point now that they will already have their painting clothes on when they come out, instead of asking if they can help and then me sending them back in to get changed first. As long as I lay a tarp down they can go at it with some primer or paint and do a reasonable job of whatever I put in front of them. I usually have to follow along behind and clean up the spots they missed, but that doesn't take long.
Like some others have mentioned, I also bought tool sets for my girls a couple years ago. The younger one got the kid's set with fake hard hat and suspenders, and some mini tools that she couldn't her herself too badly with. For my older daughter though, I put some more money into one of those multi-purpose tool sets. It has a real hammer, screwdrivers, a couple of pliers, a basic socket set, tape measure, etc, all reasonable homeowner quality. It isn't going to stock a shop or anything, but it is something that she can take with her when she goes to college and at least she will be able to set up some Ikea furniture or whatever. My younger daughter will get one like it in the next year or so.
For the OP, yes the fighting sounds familiar for sure. As soon as the older one gets an idea, the younger one wants to do it too, which gets the older one mad because she is copying. Or they both want to use the same tool at the same time, or someone took someone else's nails, or they are getting in each other's way, or one is getting sawdust or paint or dirt on the other, or any of a million other things to fight about. That is just nature for siblings. At least I assume it is since me and my brothers fought constantly too. I think your key word was "patience." You need a lot of it, and the pay back comes in tiny increments. An important thing to remember is that their interest in "building something" is only part of the reason they are there. Primarily they are there because they want to be with you. They may work independently beside you some of the time, but other times you may be better off getting them to work with you on the task you are doing.
