Hi - I understand your concern and I don't think you are being totally unrational about this as asbestos exposure isn't something to fool around with. However, more likely than not you really don't have anything to worry about. I do find it reassuring to know that your father did work on the house for years and it sounds like he knows what he is doing, i.e. checking the kitchen floor before doing work on it. There being found no asbestos in that area makes the idea that there would be asbestos anywhere else more unlikely. Unless the asbestos is out in the open it's not likely to cause a problem. Think of all the people who were born in the '20's and '30's that lived in houses with asbestos. The vast majority of those people came out unscathed. And there were people who worked in these houses without a clue of the asbestos dangers and they also have come out unscathed.
My house was built in the 1930's and I have asbestos around my pipes in my basement (in one area the asbestos is definitely doing some major crumbling). I have someone coming out tomorrow to give me a quote on removing it. In doing research over the weekend on this subject I found out that plaster walls can contain asbestos and they must be tested before removing. This has me more than a little bit concerned because there is one area in my kitchen where a big chunk of plaster fell out about 3-4 years ago. I thought nothing of it and swept it up. Since then a few more pieces have fallen out and I pick them up, throw them out, and sweep up the mess. Now I find out how dangerous this may have been. Just to get this tested will cost a minimum of $500.00.