My test to see if a hen is broody enough to trust her with eggs is that she spends two consecutive nights on the nest instead of roosting in her normal spot. One night is not enough, it has to be two consecutive nights. Someday that may fail me but it's worked so far.
You absolutely can take some eggs from the incubator and place them under a broody. How many eggs do you have in the incubator? I've given one hen as many as 16 chicks the same age withing a couple of days, some she hatched and some from an incubator. I gave another hen 15 chicks.
You have two basic ways if handling a broody hen, isolate her from the flock or let her hatch with the flock. If you isolate her, lock her up so no other chicken can get to her nest and she cannot rejoin the flock. That can be anywhere but it needs to be predator proof. A lot of people fence off a section of the coop or fix something in the run. You need a nest and room for feed and water. Keep her isolated in there until she hatches.
If you let her hatch with the flock, clearly mark which eggs you are giving her. I use a black sharpie and make two circles, one the long way and one the short so I can see at a glance which eggs belong. Then after all the other hens have laid for the day check each day and remove any eggs that do not belong. The way I do that is to reach under her and raise her up so I can see. Some people physically toss them off the nest. They normally hunch down on the floor for a while and then may go back to the nest or they may go eat, drink, and poop before they return to the nest. if she is truly broody tossing then off the nest will not cause them to break from being broody if they have been setting a few days.
It is important to check daily for new eggs. Other hens might lay in her nest. Some broody hens will raid other nests and carry eggs back to their nests. It is important that all her eggs start at the same time. Otherwise you get what we call a staggered hatch that is extremely stressful to you and often does not end all that well. Since you don't know if she has any eggs now or how long they have been there you need to start her over, either with fresh eggs or some form the incubator.