Dreaming...….I understand how awful it is to not be able to completely trust. After all, part of the advantage of having two parents, in the nest, is to be able to share the workload of caring for the young.
I agree with the others...that having a solid plan, for when you travel, is imperative. Your peace of mind, your employment and their safety depends on it.
It might be helpful to ask yourself...if you were a single parent...with the children...what would you do when traveling, away...?
My first thought, is this----Find a very competent, mature woman who has a driver's license, to be available for when you are away...to live in the home, around the clock....OR....a trusted person who you can leave the children with...in their own home, while you are away (a paid person, of course)….
****If a person is living in the home, while you are away, and anything untoward should happen...like, if he should drink....then she could be instructed to take them to a hotel, until you return...or get him to leave the house...if he will.
Now...I can imagine, that this sounds like a big mountain for you to climb! And, it is quite a task. But, still important for your peaceful functioning.
After all...lots of celebrities do this, as a normal way of life...lol....The "nanny", basically, takes care of the family.
My daughter did this as employment, during the 6 yrs. that she went to college and got a second degree...she worked as a nanny to a wealthy family, for their three kids. She practically ran the entire home... (both parents were high powered lawyers, who had very erratic schedules and were often away from the home)….Actually, after she finished school, and had hoer own professional employment...she often spent overnights and weekends with this family...for emergencies...because she was sooo attached to the kids!
I know that this might sound costly....and, it isn't cheap, I realize. But, perhaps you can discuss this with your husband, and make financial arrangements---like a special savings account for when you are away overnight or traveling. You may have to sell some things...or, cut back on some things, or he might need to take a part time job, etc...etc....
What a pain...but, I do believe that if this situation is accepted as an absolute necessity---then, it believe that it is a solvable....
If you can't find a suitable person, privately...there are agencies that will supply a person, who is bonded, that can fill this role.....