Can you explain more about this WiFi broadband.
Who is the provider?
Is the Router/modem connected by a phone cable or one like a TV cable?
Different providers have different download speeds and some are very slow compared to others. Also the use of a DSL (phone connection) compared to a "Cable" TV provider is much slower than the cable connection.
Then there is the WiFi connection between your computer and the router, they can also slow things down.
If you can, get a CAT 5 cable and try connecting the computer to the router using it and see if you get better response.
Then you may also be accessing a server at Ancestry that is busy at the time you are there, or the data just may be on a slower server to start with.
If this always happens to the same file but not others I would call Ancestry and see if they can help.