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ProudRedneck, Fruit cove is just up the road from me; I'm in St Augustine
My neighborhood has lots of oak trees -- mainly laurel oak but like live oak the leaves fall in March. I save bags of clean dry leaves that I collect from the road side before the county garden trash folks get to them. You might be able to save some bags of leaves still this year. If you can't get them when you get back message me and I will drop a couple off for you.
I mulch my back yard where my ducks free range with a 3 or 4 inch layer of leaves. The mulch looks far better than trodden down weeds and foraged in dirt!! My ducks love the leaves as they can forage for grubs in them to their hearts' content. They like flapping their wings and "blowing" the leaves; they like sliding on the leaves on the one small incline in my back garden. I actually keep two large binsful of leaves to add to the mulch later in the year when it gets worn down by ducky trampling.
In the coop/run, a layer of the leaves on the floor protects sensitive duck feet from the hardware cloth. Water will soak through the leaves and drain away into the sandy soil -- we are blessed with well drained sandy soil. But wet doesn't rise up through the leaves. My son and I both use "deep layering for the bedding from fall to spring. We just add another layer of bedding onto of any wetness and duck poop. It gets very thick and springy, and as the lower layers are composting it is warm for the ducks to sleep on in the winter. If the ducks have a water fight or otherwise saturate the bedding, I will add another layer of oak leaves to stop that wetness coming up into the pine straw bedding on top of it.
I love your coop/run set up -- and like the tarp you have now put over. My son has similar tarps on his coop/run. His curved roof with tarps opens up for accessing the inside. It's a bit of a "rough and ready" design compared to yours, but it works. He has old drawers with pine-straw/straw inside for nesting boxes although the ducks have a strong preference for one specific box and generally all lay in the same one.
My coop has a white tarp which was doubled up at one side until we got very cold weather in around November last year. I turned the tarp down to the ground to keep the ducks warm and have left it down: I don't want any passing raccoons to see my ducks. The white tarp is much more expensive than the gray tarps but it does have the advantage of being translucent and allowing light through. As all the lumber for my duck coop was repurposed second hand, I decided to invest in the white tarp so that I can see what I am doing when I am inside the coop.
I don't have a separate duck house and so I added an old kitchen wall cabinet and also bales of pine-straw for the winter -- our winters being nothing compared with our fellow duck keepers up north. One of my muscovy drakes sleeps inside the cabinet -- even now in the warmer weather -- and the other muscovy sleeps on top of the cabinet -- but he did have a straw bale up there when it was cold.
I like your set up as it is well ventilated, but there is shelter from wind and rain. Any cold nights next winter and you will be able to add straw/pine-straw bales too.
Don't worry about your ducks while you are away: I am sure your daughter will look after them. My husband and son both tend to be a bit dismissive, like your husband "they are only ducks" being a favorite refrain. But I expect your daughter will soon understand being a "duck Mama" and be very protective of your ducks.