Snow days and shooting in Manual

I got my DSLR five years ago. At the time, I was amazed with its 12 megapixels and Aperture priority mode. It gets the job done in outdoor light, but indoors, I have been pulling my hair out trying to get crisp pictures of the kids. Because they never stop moving, it is quite a challenge.

So, I have been trying to dig deeper than the various modes and I refuse to use the flash (if I ever do, I turn the photo black and white!) I have been experimenting with Manual mode and plan for a 50 mm lens in my near future. I honestly just use trial-and-error and it is getting old. But all these days indoors and the white light outside gave me some opportunities this week...

 party invitations went out this week. 

 my "office area" is coming together

 excited to have a place to switch out pictures often

 our backyard in pink light

 It is so hard to get his eyes nice and clear and then when I do, there is noise everywhere else. Help!

 Why does he wear PJs every day? Because he pulls everything else off and it's too cold for that!

 getting ready for nap time by playing dollhouse

 OK, this one was finally clear because I had tons of light and she was perfectly still.

 I finally got her to play in the snow and she loved it!

 For approximately one minute, until her hand "got wet" and then it was over

 He loved bath time all by himself today. No one to dump water on him and take his toys...

 We love a clean baby

 Part of the Easter mantle. The rest of the picture keeps coming up either noisy or blurry...so that will have to wait

 Some amazing hand-painted REAL eggs my mom got me a few years ago

I painted this one day and actually really enjoyed it. 

So, there we are. Suggestions?  Lessons, I know. I took about a billion and these were the best I got. Why do I have to pick between a blurry, noisy, or too dark photo?  WHAT WILL FIX IT ALL?!