I believe the variables that will be most helpful for you are MULTGEN and the combination of STATEFIP and COUNTY. The first step is to check whether your county is identifiable in the modern ACS samples. The Census Bureau does not actually identify county in the Public Use data, but IPUMS is able to construct some counties from the smallest geography available (PUMA in the case of the ACS samples). There is an excel spreadsheet available for download from the COUNTY codes page which shows the availability of each county.
Perhaps the easiest way to find what you are looking for is to use the Online Data Analysis tool, selecting the “ACS, 2001-2014 data” set from the menu. Since we will be using MULTGEN as our variable of interest and MULTGEN is a household level variable, will will need to make sure that we are using the household weight to make the numbers representative of the total population. So we set “Weight:” to hhwt. The Online Data Analysis tool uses the Rectangularized version of the data, so we will need to select only one person from each household (see number 2 from the Weights FAQ). We accomplish this by typing pernum(1) into the “Selection Filter(s):” box. This selects the first person from each household. We want to filter down the results even further since you are only interested in a single county, so we add (as an example, this selects for Minnesota’s Hennepin County) statefip(27) county(530) to the “Selection Filter(s):” box. Finally, since we are not interested in Group Quarters we can filter our analysis to only include households by adding gq(1,2,5) to the “Selection Filter(s):” box.
With the filter’s set up correctly, getting the percentage of households with more than one-generation is as easy as putting multgend in the “Row:” box (the d in multgend indicates we want the detailed version) and year in the “Column:” box and clicking “Run the Table”. Since you are mostly interested in adult-adult multi-generational households you can added the percentages in the 22, 31, and 32 rows for each year.
If you would prefer to use an extract, since you will be working with the data in either Excel or R I would recommend using the Select Cases option from the extract menu and select cases based on STATEFIP and GQ. This way you can limit your extract to only records from the state you are interested in and only households (GQ == 1 or 2 or 5). You can also request your extract in CSV format from the extract menu which can be easily read by both Excel or R. However, depending on the size of your state, you may go over Excel’s row limit, so I would also recommend extracting 1 year at a time.
I hope this helps.