Kitten obsessed with older cat. Older cat not impressed.

TLDR; new kitten following older cat around. Older cat's body language seems to be relaxed in kittens company, until the kitten moves, touches or surprises her and then she hisses and swats. Is this normal or do we need to take a step back with introductions?

We adopted a 14 week old spayed female kitten a month ago, and already have a 10 year old spayed female cat who we've had since she was a kitten too. We kept the kitten in the living room for the first week and brought our older cats food closer so they were eating together. We have glass patio doors in our living room and the two cats would look at each other through this- at this point the kitten would hiss but our older cat seemed very relaxed. After another week of this both cats seemed relaxed seeing each other so we tried introducing them- distracting the kitten with a feather wand and giving both cats a treat.

All seemed to be going well until we let the kitten have the run of the house. As soon as the kitten sees our older cat she follows her around. I think she wants to play as she displays lots of inquisitive and playful body language. Our older cat is not impressed and hisses when she walks past the kitten or if the kitten moves too quickly. If the kitten stays still my older cat will sit or lie down and she looks relaxed, but as soon as the kitten moves or goes to touch her she hisses, and sometimes she swats at her (the kitten usually flattens her body or shows her belly when this happens). Our older cat will also hiss and go to bite or scratch us if we try to touch her in the presence of the kitten.

Hissing and the occasional smack is as far as the behaviour goes, there haven't been any fights as the kitten either slinks off at this point or my older cat removes herself from the situation- she has a high windowsill that the kitten can't reach, and we also remove the kitten when we notice our older cat getting stressed.

The kitten is shut in the living room in the evening and overnight so my older cat gets a break. During these times she'll allow us to stroke her but will suddenly reach a point where she swats and hisses which isn't like her except for times when she's been in pain and we've touched a wound or something. I can't see any wounds and she has allowed me to stroke her all over so I think it's more of a psychological thing- maybe she can smell the kitten or thinks she hears her which is putting her on edge.

Is this normal, or is my older cat distressed? The kitten seems to be taking it all in her stride and it hasn't stopped her from continuing to approach our older cat.

Does anyone have any advice?