Stucco Gaps and Mice

Got a mice problem that I've tracked down to gaps in the stucco near the ground. What seems odd to me is that the walls are not constructed flush all the way down to the ground. In other words, near ground level, there is a 90 degree indentation of about 1-2 inches. This goes all around the house, and I don't see a reason why it's built this way (I'm not familiar with stucco or construction techniques and materials). On the underside of this indentation appears to be some kind of aluminum edging, and the mice are exploiting the poor seal between the stucco and this aluminum edging. I have also found some large openings along this underside at corners, some you could stick a baseball into. I patched up the two places where I found mice entering, but if they got in at these two spots, I would think they can tear open new gaps elsewhere.
This is a new construction house (my sister's) but the seller was the general contractor himself (not a professional) and as you'd expect is a pain to deal with. Should I go around the perimeter of the house sealing the indentation with stucco patch? I need a permanent fix to this mice problem and would appreciate any advice or similar experiences. Thanks for reading.
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Should I go around the perimeter of the house

Try eliminating the mice *in* the house first, then plug up the outside toute suite, but make sure that seam is not a vent device. If it is, you could use hardware cloth or other galv. 1/4 inch screening to patch the holes in the edging.. Trouble with just plugging holes, you may end up with starving, rotting mice bodies in wall cavities and elsewhere. I tend to use traps vs poison inside, as the latter also litters hidden places with corpses. Also, clear away obvious outside nesting areas, such as boards, tin, rubbish, where they can find shelter. Also, check cabinets and pantry for easily-got-at food items, and remove or re-box them. We use tin boxes for yummy mouse food like oats and grains, cereals. Mice can live only so long without a handy food source, but they may be using house for breeding/nesting, and foraging outside for food.
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Would you think that any hole found near the ground could be some kind of vent? There is a big one near where I found a mouse entering the house, under the overhang/indentation and in a corner. I think it might just be shoddy construction work. I'm inclined to plug up all of these kinds of openings that I can find that are not blatantly designed vents. Not sure how good an idea this is, i.e. if it might screw something else up inside the house (circulation/ventilation?).
Appreciate the advice on avoiding dead mice behind walls, etc. Unfortunately, I have not seen a mouse or signs of mice inside since I trapped two a while ago. I only hear them inside the walls and have only seen them outside burrowing in while I was spraying for ants.
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You might have a reputable contractor or a known building inspector look at the holes. If they are indeed shoddy construction, you may want to know the fix, and whether to block them or not.
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Henry wrote:

Permanent solution = Cat
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