How can.we prevent her from going into the house without us kids or the executive not knowing who that is.?
Please help me on what I can do.
There's nothing you can do while your Dad is alive unless he's willing to involve you in his estate planning.
However, the best thing you can do is educate yourself on the NH probate laws and probate procedures so you are prepared for the eventuality:
2015 New Hampshire Revised Statutes :: Title LVI - PROBATE COURTS AND DECEDENTS' ESTATES
New Hampshire Judicial Branch - Circuit Court Probate Division
Immediately upon learning of your father's death, you go to court and open probate under intestacy and ask the court to appoint you representative of the estate. The faster you do this the faster you get the authority to act on behalf of the estate and take possession of his house and his assets and secure them from the girlfriend.
Doesn't matter if he has a will or not as that can be addressed later on (unless you somehow get the original of the will at some point).
Once you have the court's written authorization in your hand you can get a locksmith, open the house, walk in, take possession, tell the girlfriend to leave and call the police to report trespass if she doesn't, and report theft/burglary if you know anything to be missing.
Any failure on your part to act immediately gives the girlfriend the opportunity to clean out the place and the longer you wait, the less you'll be able to do about it.
One more thing, if you have reason to believe that your father is losing his faculties and becoming incompetent to handle his own affairs, you can go to court and seek conservatorship over him. That, unfortunately, is an expensive and time consuming process, but something to think about if necessary.
Bottom line, though, is that as long as your father is alive and mentally competent he is free to spend all of his money on his girlfriend and give her all of his worldly possessions and there isn't anything you are likely to be able to do to prevent it.