Visiting my parents w/ the kitten

Hi everyone, I'm new here...the forums I used to be on seem to have died and I have a question.

I'm a new cat owner. My kitten, Dexter, is about 6 months old. I recently went to visit my parents for the night and brought him with me. My mother is extremely allergic to cats and they also have two dogs, so I kept him in my old room, which is unfortunately quite small. It was only for one night, and he seemed to do okay, but when we got back to my apartment, he started darting around like crazy, like maybe he had a lot of pent up kitten energy that he couldn't expend in the smaller space. He sometimes gets that way anyway, so it's possible it was just coincidence, but I have a long break from school coming up and I'd like to spend a few days at a time with my parents. So, two problems: one, is he going to get the exercise he needs in such a small space? Or, alternatively, is the small room for a few days going to be at all detrimental to his kitten-ness? And secondly, while we kept the dogs away from him, they occasionally came and sniffed around my room; one of them even whined outside my door when I was in there with the cat, and the other would sneak upstairs and just sit outside the door. I could tell it made Dexter nervous, in an offensive, hair-raised, back arched, let me at 'em kind of way, not an "I'm gonna go hide" kind of way. If there was some way to let him roam the house, I would attempt to socialize them, or at least help Dexter find some high up safe spots, but given my mother's allergies, this isn't possible. This is essentially the same question as the first: is it going to cause problems for him psychologically to be safely isolated but in close vicinity to two dogs?

Thank you all in advance!

Dexter is such a cute name for a kitty

The darting thing could be a kitten thing, but my 1+ year old cat still does it . Cats are fine in small spaces. A great toy to have for a kitten with lots of energy is Da Bird (it's a black wand with a feather on the end). Anything interactive like that is a good toy, try to play with him 15 minutes a day. That would be plenty of exercise.

I had 1 kitten with me last Thanksgiving over that break. She was almost 4 months old at that point and I just kept her in the bedroom the whole time. (My mom is allergic and has a shih tzu, but the reason I kept her in the bedroom was because I was afraid of losing her in the big house, plus I didn't want her to have to deal with meeting other animals). If a cat is in a new place, it's probably best to keep them confined to a bedroom or bathroom for a few days before letting them explore.

As for the dog...sniffing through the door is perfectly normal. If you are only there for a few days, I would just keep the cat and dog separate. I suppose you could introduce them but only do it if the dog is on a leash or if the dog is in a crate. Expect lots of hissing.

The cat doesn't really need to roam the house and would feel safer in a smaller space that it could watch over.

No he will be fine for a few days in one room. I would not bother to introduce him, but the car riding and visiting new places is very helpful. He'll be used to riding and you can take him anywhere (hotels) etc.

If you spend some time in the room with him and play with a string toy he'll have plenty of exercise. It will be nice in a way as you'll be able to bond with him at night.

Thanks for all the advice! I feel much better about bringing him. I don't see much reason to try and introduce him to the dogs, I doubt they'll be too receptive and he's not going to be able to have free run anyway.