BEClem, Do you have a thread on the forum? I did read the thread over in Newcomers and think you may get more responses if you have one in the MLC Forum. However, that is your call to decide whether to post one here or not.
I'm going to try to provide you w/a couple of responses on this thread, but I would really like to see a thread posted in MLC so that we can see your entire story and then you can have a journal to refer back to about you and your situation. Okay?
Anyone can be a distance/pursuer. It doesn't necessarily mean the wife has to be the pursuer. Both the husband and wife can switch up the dynamics at any time because of what his transpiring in their lives. What you have described about you and your wife isn't unique...but you are still pursuing in a way. Sure, you aren't talking to her about the relationship, but your actions are saying something different. Instead of doing the chores around the home when you are there, I suggest that you just leave them be. Your actions are still telling her that you want her back and will do anything to prove that your depression has lifted. Even though you don't draw attention to those completed chores, she is very well aware of what you are doing.
So, instead of doing the chores, spend the time w/your children. Do things that are fun w/the children. Get out of the house, take them somewhere and just spend quality time w/them. As for the chores, since she's living in the home, that is now her responsibility to take care of them. If she should ask you to help out w/them, then fine...unless the toilet is overflowing or the air conditioning is on the fritz when you are there...leave the chores alone. She can't miss you if you are continuing to do things for her.
As for showing her that your depression has lifted, start living your life. Find hobbies and outside activities that will help take your mind off of the situation. Get together w/friends and actually starting living again. Actions of this nature say more than doing the chores.
Live your life for YOU and your children. Give your wife the time and space she requires and allow her to figure things out for herself and that includes the chores in the space that she is living.