Hi, I'd like to help you with your question.
It is very common for women to experience a drop in sex drive after giving birth. She most likely has not lost interest in sex, she is just too tired to put it high on her priority list. It has been 3 years since she gave birth, but the responsibilities of having a child and running after a toddler are exhausting.
Some of the more common reasons women lose interest in sex is because of the tiredness and energy it takes to care for children. They simply are too caught up in child care to think of anything else. The other reason is stress. The amount of attention it takes to raise children gives a parent little time to do anything to care for themselves. They do not get any down time and therefore lose energy for any activities other than rest when they do have the time.
Another factor may be the amount of work your wife is dealing with. Are you able to care for your child so she can do something else? Can you deal with some of the housework? This may enable her to get time to care for herself and feel better.
She may also feel sensitive about her body. Women who give birth often lose the firmness and muscles they had before childbirth. They may have no time or energy to diet or exercise, compounding how badly they feel.
What you can do is work on helping her out. Take over for her one night so she can go out. Give her gift cards to get her nails and hair done. Bring home dinner a couple of nights a week. Talk with her and allow her to vent. Give her opportunities for adult talk if she is a stay at home mother. In other words, treat her well and let her know you think she is special.
Try to set up date nights. Get a babysitter and take her out. If you can, plan a short weekend get away, just the two of you. By taking action, you show your wife you care and that you desire her.
Go slowly. She needs time to adjust to thinking about your relationship again as primary. Here are some resources to help you:
Is There Sex After Childbirth?: A Couple's Guide to Survival Through Pregnancy, Birth and Parenthood by Juliet Rix
And Baby Makes Three: The Six-Step Plan for Preserving Marital Intimacy and Rekindling Romance After Baby Arrives by John Gottman Ph.D. and Julie Schwartz Gottman
Confessions of a Naughty Mommy: How I Found My Lost Libido by Heidi Raykeil
You can find these books on Amazon.com or your local library may have them for you.
I hope this helps you,
I have not heard from you. Did you have more questions or want clarification?