I forgot to add that both of our cats have been "fixed" before we got them.
If you can get the new cats gathered up, vaccination is always a good idea. The vet may want to test them first, or may just vaccinate since they are feral.
Your barn cats should be okay from the diseases they were vaccinated against, but the new kitties may have other infections they could transmit. A vet check for the new kitties would be a great idea, if you can get them there.
You might also look into whether there is a feral-cat group in your area. (Some places have good ones and some don't have any.) The best will come and trap, spay/neuter, vaccinate, and then release back to where you are, meaning a feral colony would still be around but at least you would not have to worry about kittens in the spring and the kind of diseases that can be vaccinated against.
If the kitties are all living on your property, pretty soon, legally they are your animals. So, do your best to locate some feral-animal help and advice.
The philosophy on feral cats is to trap them and spay or neuter, and then release them back where they were and monitor them, rather than haul them off to be killed. If you can find a good outfit who does neuter and release and monitor, they would be a real help.