For the ants problem: they hate cinnamon. Really hate it. We had a few come into our house, followed their trail and put cinnamon along the wall/floor where they went in and out. Haven't come back since then, and that is eight years ago. So, if you can somehow make a cinnamon paste (perhaps a bit of glue and a lot of cinnamon) to put where the line attaches to the tree that should work. Just renew it every now and again.
As for line drying...
I love the idea of it, but seeing as I live in Sweden where summers are short and the idea of a covered porch of some reason has never really caught on line drying outside is something of a rare occurrence in my home. Nothing is made better by the laundry room being down in the cellar, and me having to carry the heavy, wet laundry first up the cellar stairs, then out the front and round the back to the very end of our garden to hang it. And then keep an eye on the weather, hoping there will not be rain...and at the first patter of drops against my window panes rush outside to try to save the laundry from getting soaked. On top of that, I am allergic. It is not as bad as it used to be when I was smaller and we lived in the city, but it is bad enough that I really don't want to wear line dried clothes nor sleep on line dried sheets if I can avoid it.
So, in my family, we hang dry inside. We have this collapsible drying rack that holds about two machines worth of laundry. I'm thinking, once we get money to renovate our leaking roof, that it would be nice to add a few pull out drying lines to the attic like they had in the old days. Making the most use of the space there (since the cellar is really not an option, because of the problems of keeping it dry as it is. Things take forever to dry down there, so we usually utilize the space in our dining room).
Generally, I think air drying things much better than tumble drying. For one thing, socks don't tend to get lost in the same way (I hang them together, and pair them up as they have dried). For another, fibres in clothes don't take such a beating which means they last longer. It is really only the towels and bed clothes that gets thrown in the tumble dryer in my home, simply because it is easy, saves time and saves space on the drying rack.