The problem is that my HDTV has only one coaxial antenna input,
That is normal.
so I need to use HDMI for this second antenna input.
No, you don't.
The antenna gets priority for the antenna jack if the TV is to use the antenna. If your SD output from the VIP222 is on analog channel 3 or 4, then use the HLSJ as recommended by ctdish unless the exception below applies. Do NOT use a reversed splitter!!! The HLSJ will NOT strip UHF through the HI port plus, as ctdish noted, you may turn your system into an unintentional radiator.
Exception: Selection of an antenna is best done based upon what the technical and signal requirements might be, not how much hype and bull$hit a marketing company like Mohu can pump out. If you have local stations that operate on real channe2-6 that you want to receive with the antenna, than the HLSJ will not work. Since there's only about 35-40 full power low-VHF stations in the whole country, it's not terrible common. There are ways to work around this issue, if necessary.
However, if you can post a link to your exact address TVFool plot, we'll be able to make an informed recommendation to you so you can understand your options in selecting a technically appropriate antenna. http://www.tvfool.com/?option=com_wrapper&Itemid=29
Make sure that Google's Maps can accurately resolve your address first.Edited by ProjectSHO89 - 9/28/13 at 2:13pm