I think every good mom asks herself if she is a good mom! The fact that you care if you are a good mom or not means you are, or are on the right track. I've asked myself countless times the very same thing!! You are not alone!!
So many times we see "examples" of perfect moms who spend the whole day cultivating their little ones with games, activities, and playing with them. Nice thought, and maybe some individuals can pull it off... I certainly can't. There are many times I tell my kids to go downstairs and watch a movie or go play by themselves. I used to think I was a bad mom for this, but now I know that is just insecurity talking.
What IS important is that I DO make some time for them, even if it is not constant. We snuggle while watching a movie, talk together about different things, occasionally color together (coloring books are FUN, haha!), sometimes make cookies, and sometimes read. We never do all in one day or even one every day. One thing you can make constant are hugs, kisses, and I love yous. If you can show them love, even for 5 minute chunks, you can fill up their little hearts enough to last until the next 5 minute chunk.
The part time day care and exercise will be SOOOO good for you!! You will get a break, some honest-to-God Mommy time! Go paint your nails, do a little kid-free cleaning, read a good book, and revel in your time for yourself. You will feel so much better when you pick them up and see their cute little faces! Take care of you, put them to bed early and have time to yourself, and then get some rest yourself! In order to take care of them, you must take care of you too!!
A schedule is good, just try not to start off too strict or structured. Pick a few big points during the day and then work from there. A big help for me was FlyLady.net. Very, VERY helpful! (It may look cheesy to you to start with, but bear with it, it is the most helpful thing I have ever come across!)
Keep your chin up, hun. I've been there (almost to the letter, depression, sending them away, not wanting to do ANYTHING, and dealing with massive amounts of guilt about it all, which of course made me MORE depressed!) and there IS a light at the end of the tunnel. Just take one little step toward what you want, and keep on stepping and eventually it will get better!
PS. I agree with the other poster who said if you need help don't be afraid to get it. There is no rule that says you have to do it all, all on your own. :)