First of all I would look very carefully round the outside of your property , to see if there are any holes or cracks through which the mice can get in. Like for example where pipes go from the sink to an outside drain and so on .If there are any to be found seal these up with cement.That way you are preventing others getting in.
As you seem to have a number in the house , they may be nesting inside already , so a really good search of cupboards , under the sink , food cupboards top shelves and so on.Get rid of any unwanted rubbish as you go , old newspapers and so on which could be used to make nests.Lay your traps as you do each night.
Look for holes and cracks again as you go and seal these up Be really vigilant about leaving anything out at night as well which might be food for them..
Am writing this from my own experience of last year , I became almost paranoid about the blighters.Still I saw it as a challenge and was determined to win , and the clearing out did me good.
Like you I have a wee dog who is anti cat greatly , so I arranged with my son to borrow his cat each night on a sleep over and he would take my dog to sleep at his house.We did this for 3 weeks and the mice seemed to get the message . But what a performance it all was , have not had any since, but it doesn't stop me from looking , but think blocking things up, and clearing stuff out was the real key to the problem.
The very best of luck .Brenda.