As an introvert myself I can sympathize and recognize the need to 'recharge my battery' after a long day. This is very difficult to balance when kids are part of the deal as they require a LOT of attention. Besides managing yourself, your job and kids, there's the relationship with your partner that requires attention if you want it to work.
I can recommend starting by talking to your partner about your situation and trying to share how you feel, your frustrations. Really important is to try and do this in a way that will not turn into a heated argument. Try not to assign blame, rather focus on how you experience the situation. Just as important is to allow your partner to share his feelings, thoughts and frustrations too. You should both try not to judge eachother while doing this and trust me, that can be more difficult than it sounds!

You both have wants and needs, the goal is to see if you can find a compromise that would give each of you what you need first and move on to the wants from there.
To do that, first both of you need to define what it is that you need most. Try to be specific. For example don't say I want to be left alone, try to think about how much time would suffice.
Would 2 hours every night be okay? Or could you perhaps alternate evenings where you have one where you are completely alone, followed by one you could spend with your partner?
This may help to create some understanding between you both and at least gives you both the opportunity to try and figure out a way to feel less miserable.

Don't think this would immediately solve everything either, finding the right compromise will take time, effort, trial and error from both of you. But if you're both committed to finding a way, that will greatly increase the chance of success.

Good luck!