I female cat lives with me, a few months ago she got pregnant and had
two beautiful male kitten. The kitten are 8 months old now, and still
live with me and their mom. Last night a foreign cat came to my home
and the mother got mad and attacked the intruder, which ran away, but
then the mom attacked her babies.

We separated them and a few hours later they were calmed. We joined
them again and they were like nothing happened. Later, in the morning
my fiance woke up and opened the door of the laundryroom to get a
towel and got in the shower leaving the door of the laundry room
opened (from this room the foreign cat got in the house). I was still
in bed, so no one knows what really happened, but the cats started to
fight again.

Is this behavior normal? is there anyway they can live together? or
the mom always fight her children so they leave the place? what can I
do so they can live in harmony?

I will appreciate all your advices. Thanks in advance.