My name is ***** ***** I will be happy to help you.
I'm so sorry you've been experiencing this problem for so long; I can only imagine your frustration.
From your description, it is my opinion that yes, the mice are breeding and that's why you're seeing more or seeing them at all, and yes, they are mostly the same mice. If the poisons put down by you and the professional exterminator are guaranteed to kill the mice, there's not reason this shouldn't be happening, unless the poison is not strong enough. They may be immune to it, if it's been used for a long time, to get rid of mice, and they may be rejecting the wheat based one, because they don't like the taste or they can smell that it is dangerous to them.
The rodenticides that are used in the U.S. can contain different types of poisons. Some work faster than others. Here is additional information about how these rodenticides work.
The bromadiolone based poisons you're using should be causing internal hemorrhaging and killing the mice, but as you can see, at the link above, this is a lengthy process and that may be why, as you suspect, you're seeing the same mice over a period of time. As you can read in the link above, there are faster ways to kill the mice in as little as 2 days. Try to find the rodenticides that kill more quickly, in your area or ask the exterminator to get it (perhaps use a different exterminator).
Instead of cotton wool, stuffing any cracks/openings with steel wool (like 'Brillo' soap pads for washing dishes/pots, but without the soap) is more effective, as the mice can't get through the tangle of steel wool.
Make sure no food or trash is left out on counters or in the house and constantly vacuum the floors to get rid of crumbs. For foods in your cupboards, in boxes, either refrigerate them or put them in plastic ziploc bags, so the cardboard can't be chewed at to get to the food.
The most important thing now, is to find where they are coming in and if they are living in the walls, a stronger approach by an experienced exterminator who deals with mice, will be necessary.
I wish you much good luck and hope over a short period of time, you will finally be rid of this problem and take precautions so it doesn't happen again!
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