I had my tubes tied right after my c-section with myDD. Everything went well. But if I had a choice, I wouldn't do it again. Ever since my daughter was born I have had increased issues with hormone balance, menstrual pain, etc.
I don't want to scare you, but do your homework before you have this procedure. Most women have no complications after the tubal ligation. But a number of women have issues that fall into the category of Post Tubal Ligation Syndrome. Women who have had hormone (miscarriage, low thyroid, infertility, irregular periods, etc.) or chronic illnesses or on going issues in the past are at higher risk for PTLS.
I wish I would have known about PTLS before I had my tubal.
Your surgery should be fine and you will be fine. But it's the long term after effects that you need to look at. My daughter is almost 3 years old and I just had my uterus removed on Wednesday due to heavy bleeding and unbearable pain. Prior to getting preggo with my daughter I had minor issues with low thyroid and adrenal output for about 3 years. Then after my daughter was born and after my tubal my thyroid issues got worse, I developed Fibromyalgia (a chronic pain disease), and had very painful periods ever since.
I would also recommend having your spouse get snipped. Far less invasive of a procedure for him, and it doesn't affect his hormones at all. Looking back at all I have gone through in the last 3 years, hubby says he would have gotten snipped if he had known then about PTLS and the affects it would have had on me. And this is the guy who practically jumped out of his seat for joy when the OB told us I had to have a c-section. We had previously agreed that if I had to have a c-section that I would get the tubal done at the same time. If I delivered vaginally he would have to get snipped.
Also, congrats on your new baby! Hope you are both doing well.
I also get nervous about the general anesthesia and I have been through 7 major surgeries. It is scarey to think that you might not wake up from it, who would take care of your kids, etc. With every surgery I am not scared for myself, but for my family and how they would be if something happened to me. My best advice is to pray. I believe in God and I pray a lot leading up to surgery. I also share my concerns with my hubby, my best friend, my sister, and my Mom (the people who are my innermost circle of support). Don't hold it in, lean on those around you that you trust. Going through surgery and recovery is a stressful time for a person. I usually try to focus on the 6 week post surgery mark (the standard time where you can get back to strenous physical activity after a surgery) and pick one thing that I will get to do once I get the all clear from my doctor. For this surgery I am focused on being excited about getting back to Yoga after a 4 year hiatus because of health issues. I can't wait to get back to it :).
Good Luck!