It is a swarm that I got about two weeks ago, but most of their room is foundation. and they have been up against that north wall of the hive since
Sounds like hive is too small to gather honey.
If there is brood in it should I move the brood to the center of the hive?
When bees take a place in the hive, there is no need to put it another way. They like to try correct situation. I have done that mistake many times.
If there is no brood I will combine it with my nuc that I am pretty sure has queen, with the newspaper method. they seem to bee flying normally
If you have a nuc, it is better to put them together. It is cruel but really wise. As two hives are not able to gather honey. When you join them now,it developes well and you will get honey this summer. In July you can take a nuc from that big hive.
If hive is under 2 Langstroth boxes, it's development is slow.
Take a swarm queen and kill it. Next day you put together with nuc. For a night put the screen between tohose two hive and they will become same odor. Then just put them together. You can put nuc queen under little age taht nothing harm will happen. When I join two even hives, I do not use any screens or papers. But when queen is valuable, I do not take a risk.
You must get rid of that swarming restless queen. Otherwise you have all the time conflicts with your hive. And it will swarm next year. When I started my beekeeping I buyed tens of swarms and I found that if I put them together that they occupy 2 Langstroth boxes, it will gather 80 lbs honey in 1,5 month. Our summer is shorter than yours.
If I had 10 lbs swarm, it was able to gather 100-120 lbs honey.
4 lbs swarm = 1 langstroth box is too slow to develope. There is no space for brood and honey. Swarms are really eager to gather honey but when box is full of larvas, they are not able to do nothing elese than feed them.
It takes 1,5 month that larvas collect honey as field bees.
I know that most of hobby beekeepers are not able to do trick I mentioned. So they have all the time too smal hives, they collect hive full of honey and they swarm and run away. They never get good yields. They keep they swarming queen daugters and beekeeping is mere challenge.
When you have really good hive, you can take from there a couple of nucs in July. Then before autumn you can take a couple brood frames from main hive and give them to nucs. You will have good colonies for winter.
I have passed just now "dead point" in some hives. After winter a couple of hives were coffee cup size. I gived them brood frames in April, and now those are full of brood. Soon I give them another box under brood. They will gather honey normally in July when we have main honey flow.