>I would like to take a frame from the Itilians and Carniolians and start another hive and let them raise their own queen. (or buy a new queen) Total we will have 4 hives as my father in law is getting two also. I am not concerned with honey this year but would like to increase in that manner. Will it work?
Sure. I would take a frame of open brood (with eggs to raise a queen from) and two frames of emerging brood or just capped brood and two frames of honey and pollen and put them in the nuc. Come back in four days and destroy any CAPPED queen cells because they were more than three days from being layed when they decided to make them into queens, so they are underfed. Leave the open ones.
>And how many times can I take a frame of brood from each hive and not really hurt them to make these increases? I will start each increase in the Nuc.
Evey hive is an individual. The difference between a poor hive, a mediocore hive, a good hive, and a booming hive are geometric in proportion. A booming hive you might be able to take a frame of brood a day and it not slow them down much. For a poor hive, one frame all year may be a setback that will take them weeks to recover from.
Those two are extrememes, but both are common enough that I can't say how often you can do it. But as long as the hive as a deep and a half full of brood (or two mediums) they won't miss a frame of brood for very long.
As long as there is a full deep or a medium and a half they will be able to recover quickly enough.
Does that help?