I've recently got a 7 week old kitten and is worried about its relationship with my other pets?

The first few weeks you have a new cat it's perfectly normal for the older cat to hiss and sometimes even bat at the new comer just to ert his dominance. Give it some time and within a few weeks things should have settled down. When i got my kitten my older cat used to shove him off the cat tree or the bed, but now he takes care of him like he was his own, so I wouldn't worry. As for the dog it's normal for kittens who have never been exposed (or even if they have) to be scared of dogs you just need to slowly and carefully introduce them to each other, don't rush and don't try to get them to close to each other at first. When your kitten is ready and fully understands that the dog is not a threat he'll except her presence. He may not like her but they shouldn't fight. It can take up to months for your cat to get used to dogs so as I said don't rush. There really isn't anything you can do to help them along, things will usually work out naturally however you do need to supervise just to make sure no fighting occurs but other than that let the animals meet each other themselves. And yes, older cats do not normally fight with kittens (they may bat at them or hiss just to show that they are dominant) but usually they will adopt the kitten and act like something of a parent to him. Best of luck(: