If he doesn't move the troops to province center or meet your troops, you remain at peace.
If you encircle a decent amount of his troops, he will probably try to break out which would start a war. You could offer him a path out and give him temporary right of way from diplomacy screen as long as he is going along that path. In some cases he just needs to clear a province center so he has a clear path out of your provinces.

What you call the "second nation" is what I usually call the third nation or third party.


As Lawrence said above: In this case it is important to remember that it takes action or motion to attack. Armies at rest will tend to stay at rest as long as nobody moves.

It also helps to remember what causes declaration of war. War is triggered when you invade only when you encounter units or the province center. You can match along a vacant road and as long as you stay 5 km away from the province center or the owners armies, there will be no war.


If the third party has troops on one of the province roads you will remain at peace until your units encounter theirs after you have taken ownership of the province, or if they venture out and encounter your province center or units and attack them. At this point you could Set your relation with them to Right Of Way, and that will give them permission to be on your land avoiding a war unless they give an attack order on your units or province.


Now even if the third party occupies the province center but the province owner has no troops there, you can march right in to the province and capture the province center. If the province center was the endpoint of your move or attack order then capturing the province will finish the order and your units will halt. You will then be in a standoff situation with the third party. If you move then your units will encounter those without permission (ROW) to be on your property and you will attack them causing them to defend themselves. If they move first then that will cause an attack on your units and your units will defend. *note that this mechanic works the same even if you are already at war with the third party, and even if the province has a fort. You can grab the province and the fort right out from under the noses of the third party.