That does sound exhausting! Being an introvert really feeds your situation. You stated you love your job, but is there any possibility of working part time?
How old are your children? My girls are up and out now, but I so remember their "neediness" (my word). Especially at the end of the day. I really only worked part time after they were born, but oh, around dinnertime was fierce to survive! On one hand, I loved it, but there were times I wished someone else could cater to their needs. Good for your health and psyche that you can get a run in occasionally.
I don't know what to say about the friend thing. When my kids were little, the phone was my lifeline. Having girlfriends kept me sane! Always helped to know someone else could relate to what I was (am) going through.
Anyway, I'm rambling. Maybe someone else will have better answers. I'm glad you posted!
Being an introvert is tough because society sort of gives the side eye when we say "I just need some alone time." Is there a place in your house you can escape for like 30 minutes a day and tell you H to keep the kids away?
I can commiserate, especially with regards to a few good friends that I only speak to once or twice a year. In fact, I would say I really only have one good friend and the last time I spoke to her was this past May.
It sounds like you've been through a lot of stress lately, which explains why you're craving so much recharge time. My therapist has been encouraging me to make sure I'm taking care of myself - getting away for alone time and making time to be creative.
It's hard to do when I feel like I have so many other things to focus on and so many other people to take care of, but it really is important. (((hugs))) I hope you can get so good recharge time soon!