You started with 2 four frame nucs that you put in 10 frame deeps. I assume you were feeding, and the bees were working peaches and plums. How did they look at two weeks? Had they drawn out their frames? Did you add a second deep at that time? Then, at about three weeks, you had a swarm. If you didn't add a second deep, this might be the cause of the swarm. Here in the Mid-west, we would usually add a second deep when the bees had drawn out 8 of the 10 frames in the first deep. This gives them space so that, hopefully, they don't swarm.
Sounds like you handled the first swarm perfectly!! Adding a frame of new brood to a swarm will usually secure the queen in the hive. Then you had two more swarms!! Were they from the same hive?
Yes, you can combine the two small hives, but one of the queens will have to go. You might watch them for a while to see which queen is the better, then do a combine.
But it sounds like you need more equipment. My guess from what I read here is the reason your getting the swarms is because the hives are doing too well and expanding faster then you can keep up with them! A lot of beeks would be happy to be in your position!

Sounds like you may have had more nectar/honey filling up your newly drawn frames than there was room for the queen to lay. I think your initial swarming problem was due to lack of space for the incoming nectar. Swarming is a response to lack of available space/cells for the queen to lay eggs. There is also the possiblility that one of these swarms are actually from another area and not from your hive. The smell of hive equipment will attract scout bees to your area and you may occassionally see swarms come land in your area as well as swarms come from your hives. If you leave a hive setup with frames inside, you may come home one day to find a swarm has setup shop inside that empty hive.
Yes you can combine these two into one hive, but I recommend adding another hive body (whether you are using 2 deep or 1 deep and one medium hive body) and then you need to manage space further by placing honey supers when these hive bodies fill up.