I am not certain about this one. Cats are territorial animals, and when the
older cat returns home it may take things worse then if he was in when the
kitten arrives. I wouldn;t do it when older one is at the vets, let him come
back and relax at his own territory after the op, rather then feeling doubly
miserable, as in being in op pain, as well as dealing with territory
"occupied" by a stranger!

That is always an issue to consider, unless you know the kitten came from a
good home/shelter and has a clean bill of health.

that problem.. I have four >males and one female.  When neutered young, the
whole male / female thing really doesn't matter

Agreed. i got 2 boys and 2 girls. Tigger was done before he riched "puberty"
at 6 months old, so I don;t think he is bothered with male/female issues. He
just wanna play. And any kitten is more then welcome!

Maybe at first, but I really never had any problems with 1 litter box, as
long as it is kept clean. I would say kitten needs more litter boxzes only
if your flat is bigger and kitten might not reach the box on time.

I understand that you have the facilities to keep them apart. However, I
don;t think that's necessary really, as you are just prolonging the obvious.
What I've done in previous (small) flat is to bring the kitten in, take
her/him to the vets the same/next day to get vaccinations and flea
treatment, then let them mingle. If it has to stay apart form a night, I put
the new kitten in the bathroom/kitchen. Most tests results are provided the
same day, so you can easily come back from vets with kitten ready to mingle.

I never kept cats in separate rooms for a period of time. I also never had
problems with cats adjusting with each other apart from normal teething
problems(some growls, some hisses, some punches even from a resident cat).
If anything, I believe the adjustment this way took less then if you were
keeping the cats (as mostly advised), in separate rooms for days and
prolonging what will happen anyways. Just let them get to know each other,
and don;t interfere, unless is life threatening, which with the kitten won;t
happen. Most animal species simply don;t kill the youngsters. They will give
them a punch or kick or a bite, but all as a training method not really to
hurt them. They are just teaching them the lesson and telling them when they
go too far. Just make sure you give more attention to the existing then a
new cat,and lots of bribes, so the older cat associate new kitten with good
stuff. Some introductions could last 2 days. Some can take a week or two.
Separate rooms will only prolong the period for another 2-3 weeks. I don;t
see the point. Perhaps only if you can;t be there, put them in separate
rooms, but together as soon as they can be supervised.

If the introduction is taking too long in your opinion, you may wanna make
the cats smell the same. The reason they are unhappy is mainly the
difference in smell. So what I generally did, is to weather give them a bath
with same shampoo(I know-you may wanna wear long sleeves :)) or simply pour
some tuna brine onto them both. Not only your house will smell - well- stink
on fish, but also you might get two equally smelling kitties who might even
lick each other off,  or this will at least ease up the introduction.

I also want to suggest that since you have very young kids, you need to get
a kitten that is quite dominant and playful. Do not under any circumstances
get a timid or shy kitten. The kids will only scare it when they are yelling
and screaming and running around the house. Also make sure you give your
kids proper training on how to treat new kitten, although I'm sure you;ve
done that when older kitten came along. I do have to point this out however
to everyone, as we all know, and with all due respect,  the kids in general
are not really famous for being kind, quiet or considerate :) therefore tend
to often stress out the resident cat. The stress can cause the cat to leave
home for good. Surely no one wants that.

As for the kitten's age, many people here will tell you 6-7 weeks is too
young to separate from the mother. Perhaps leave the kitten with her if you
can at least until is 8 weeks old, and most people will advise 12 weeks old.

Best wishes

Gee, Tiara, Shadow, Tigger and Charlie
with QT in our hearts