HP 7740 will not redirect from remote computer

[LuckyEnough]

I telecommute.  I operate locally on Computer A laptop with the OfficeJet 7740 at my location.  I remotely login from that computer to Computer B  laptop via the Company Microsoft Exchange Network at my office.   I need to RDP from that network to my home (7740) printer.  For days my IT staff has tried downloading multiple drivers to get this to work with no luck.   They are professional and skilled at dealing with network/computer issues (way more so than I am) and have in each case made sure that both Computers A & B  (both Windows 7 64-bit) have the same drivers and software.  The print jobs will show up in the 7740 queue on Computer B, says it is printing and then disappear as if the print job had successfully executed.  The problem is that the print job never reaches the 7740 printer.   The ideal situation is that the printer operate wirelessly so my other home devices/computers have access to the printer also but I did (as a possible solution)  try to ethernet connect the printer to my in-house modem and network just to see if it made any difference.  It did not.  Unfortunately the manual says it has to operate either as wireless or wired but not both.    

This problem is not unique to this HP model.  I found multiple blogs on this site as well as the internet regarding other HP models, some with EXACTLY the same problem but the "fixes" are all across the board.   C'mon HP!   This is NOT an unusual working world scenario but you seem to have an abundance of printers that have this problem as opposed to other manufacturers.   I had an HP Pro 8600 that worked fine right out of the box for about a year in this scenario with no issues and then had to take my laptop A out of town.  When I returned and tried to re-setup the formerly working setup, it would no longer work.  As far as I can see there were no updates or changes to either the laptop or either Home or Office Network to cause this now "inoperable" printing scenario.    After days and hours of trying to get back to 'square one", I went out and bought the 7740 as a replacement.    

Right now the IT department is basically telling me to return the printer and buy another manufacturer's printer.  Is this how you want your customers to respond to a very significant business problem for those of us that telecommute or is there actually a solution out there somewhere?    Also it should be noted that with the 8600 I was able to hard wire it directly into my modem and it would still accept a wireless job so I seem to be going backward.   It seems ridiculous that I had to "scrap" a perfectly good 8600 printer except that I could no longer get it to RDP.   I am not happy about that but after a week with no printing I am just about desperate...any suggestions? 

[MKazi]

@ LuckyEnough

I have escalated your concern to HP’s Support Team in your region to have it reviewed for available options, if any. You should be contacted within 4 business days (Excluding holidays & Weekends).

Response times may vary by region. Please send a Private Message, if you aren’t contacted within 4-5 business days.