I can imagine that it looks difficult to balance Kapha without aggravating Vata. Have you tried anything yet? Did it have any effects?
As a general tip I'd say you should try to stay warm: avoid cold weather or workplaces, take care your clothing is warm enough and eat warm/hot and easy to digest foods (in Ayurveda foods are not only hot or cold in temperature but also have a warm or cold quality: Chilli and Pepper are hot, while mint is cold) and reduce your intake of cold foods (don't ban them completely as this will only make you crave them and overwrite your bodies natural cravings that should tell you what is best for you at the moment.) Ginger and Turmeric should do you good: try to infuse some handwarm water with it to drink if you like the taste. As for food (Ayurveda considers food the main source of health or harm so you'd usually first adjust your diet and observe what is good for you before you try herbs or any other treatment), right at the bottom is a table that states which tastes will aggravate or balance which Dosha: in your case it seems to be contradictory, but that only means you shouldn't take the Kapha-balancing foods in excess and might want to focus on complex foods rather than pure ones or adjust its qualities with the preparation. (Yoghurt e.g. is more complex than sugar, combining the tastes of sweet and sour while sugar is only sweet). On the other hand you can try to boost you Pitta a bit by doing exactly the opposite as you would when trying to, but again: don't overdo.
If you don't have any Ayurvedic practitioner near you, you'll have to observe yourself carefully and see what is good for you and what not as everyone has its own unique combination of how the Doshas come to action. Try to listen to your body; it knows best what is good for you but all too often we are way too busy to listen to it...
Hope this helps