Welcome to our forum.  Your question is a good one and has been asked or implied indirectly by others in the past but not specifically.  I'll provide an answer.  From your question it sounds like you've searched and learned something about HPV and warts so please forgive me if some of this is repetitive.

Infections due to papilloma virus occur throughout the animal kingdom- there are rabbit infections, fish infections, and, of course human papilloma virus (HPV) infections.  Over 100 different  types  of HPV have been described and, interestingly different types have a high degree to tissue specificity such that the HPVs that cause hand and foot infections  almost never cause infection of genital infections and, conversely, genital infections do not cause infections at other sorts of human skin surfaces.  I say almost never because in medicine and science we are not able to say words like never or always ever as there are no absolutes and strange things happen.  Perhaps somewhere genital infection caused by the types of HPV that infect the hands have occurred but if so, I am unaware of it and I do look for such things.  Irrespective and perhaps relevant to your question, this is really not something to worry about or to let it impact your relationship with your relationship with loved ones.  I say this because the other important thing to remember is that virtually all humans will have HPV infections, nearly all such infections will resolve on their own, and well over 80% of adults will acquire genital HPV infections during there lives but these infections will be of no health consequence in the vast majority of such infections - visible genital warts are almost always no more than a cosmetic nuisance and only a tiny proportion of infections with so-called "high risk" will progress to cause pre-cancerous lesions, of which only a small proportion of which go on to cause cancer.  Further, we have a great system for detecting pre-cancerous changes due to HPV so that they can be treated to prevent the major important consequence of HPV- invasive genital tract cancer.  For the time being, as long as women get their regular PAP smears and reproductive health check ups, nearly all HPV related cancers are avoidable.  (As more an more women and men take the HPV vaccine, even these rather uncommon consequences will get rare and rare).

As a result of what I've said above, there is no reason to worry about transmission of HPV infections occurring at other body sites to the genitals nor any reason to worry about genital HPV infections being transmitted to others or other body sites on your hands. 

I hope these comments are helpful.  If not, please let me know and perhaps I can help.  EWH 

Thank you.  I'm pleased the information I provided has been helpful.  Your understanding of what you need not worry about the transfer of hand warts to the genitals (or vis versa) is correct.

The information I made about tissue specificity is the result of biopsies and testing of literally tens of thousands of warts and HPV infections over the years as research was systematically carried out exploring the relationship between HPV and warts, HPV type and wart location, etc.  Such studies, most of which have been done over the past two decades have informed  our understanding of HPV tissue specificity. 

Research about HPV transmission, including transmission on inanimate objects is ongoing and there are elements of this process that are still not fully understood.  Most scientists believe that there are rare cases in which HPV has been transmitted through contact with inanimate objects but they also agree that such transmission is quite rare and far, far rarer than transmission through direct contact.  I know of no data on how long HPV might survive on an inanimate object - this would be difficult to do because of technical problems and the need to detect HPV by detection of DNA rather than growing the virus.  The DNA from dead virus would be detected in the same way as viable virus. 

The issue of HPV persistence is likewise a topic of ongoing research.  The immune system tends to naturally control nearly all HPV infections, making warts go away and HPV to be undetectable or detectable only by highly sensitive tests which are not used clinically.  As the immune system does its work, signs of infection go away but HPV DNA while detectable, does not seem to be transmissible or active.  Thus HPV does not periodically recur in the way that herpes infections might.

I hope these additional comments are helpful.  You are getting into the realm of complicated, ongoing research.  I urge you not to get too worried about the "what ifs".  EWH

Thanks for the additional context.  I'm pleased my comments have been helpful.  As I've already said, in the vast majority of persons warts are merely a nuisance so one might ask the question of just how much one should worry about warts that you are not even aware you have.  I would argue not at all.  As for your encounter in the waiting room, what was described was a very rare condition called recurring respiratory papillomatosis which is estimated to occur in somewhat between 2 and 5 out over every 100,000 live birth (i.e. less than 1/1000th of 1%), making many other problems far more common.  This too is something I would urge you not to worry about. 

With regard to your follow-up questions:

1.  I do not see a need for you to wear gloves while caring for/touching your children.  Better to deal with the tiny chance that they might et a wart than to deprive them of a mother's touch.

2.Simiallry, I would not worry about transmission of warts on inanimate objects.  If this occurred with any serious frequency we would all be covered with warts.

3.  Certainly no reason to worry about handling/washing your children's clothing and laundry

This is my third response to your questions.  I'm sorry you have had to worry so much about this but understand how this can happen.  I hope that with these additional assurances you will be able to move forward without concern.  If there are additional questions, you will need to stat a new question as our Forum guidelines and practicality allow us to only provide three responses per question.  Take care and please don't worry.  EWH