I have been feeding a "family" of stray cats since the start of the summer. It was a mother cat and her two kittens. Lately we haven't seen one of the kittens and we rarely see the mother. Well one of the kittens comes around our house every night and sleeps at our door. We have a cat already so I'm concerned about letting this stray kitten inside without knowing what the stray may be carrying.

We want to somehow trap the kitten so that we can take her/him to the vet and get them checked out, cleaned up, etc but the kitten comes after the vet is closed.

Would it be safe to bring the cat into the home? How would we even trap to begin with? My last housecat was a stray and he followed us inside and thankfully did not have an diseases - he didn't even have fleas. What could this other cat have? Any help would be appreciated.

It is not a good idea to bring him in without a vet check first. Earmite, fleas, distemper etc...
If he will allow you to pet him, just get a pet carrier and put him in that along with some blankets also cover the cage to keep out the cold air. If he is not trusting,
CAll your local cat rescue group they may allow you to borrow a trap so that you can trap him. They will probably take in the mom and the rest of the kittens, luckily she should not go into heat until late Jan or early Feb.

I've rescued 2 stray kittens previously. They were so adorable. One of them (who I found trying to escape a garbage pale) was just so eager to get helped that it actually came to me and didn't mind me holding her. I then took her to the vet and got her shots and everything and I have still have her. The other one was a bit tougher. He was in my friends yard. Her yard connects to a big open field. I had to lure him in with food. He looked like he was starving and recently lost a fight. He was so young :( but anyway I took him to the vet too and cleaned him up and everything and then gave him to a friend. If you are concerned about the 2 cats fighting, bring a small box with litter and small bowls for food and water into your room or somewhere with a door to keep the cats for meeting. I hope this helped :)