You answered this question by saying you are spending more time with your family/children...
However, I would suggest that doesn't happen to "fix a problem". It's OK for now - I remember FORCING myself to spend time with my kids initially. I wanted to put my energy on the marriage problems.
However, I'm now so glad I "forced" myself - because at this point, there is nothing I'd rather do than be with them.
You need patience, first and foremost. This is definitely a marathon, not a sprint.
I would suggest that what you're doing is good if W is noticing it, and mentioning to MIL. There are stages they go through - I don't recall exactly, but it's something like: Stage 1: See changes, think it's fake Stage 2: See changes continue, but don't want to get their hopes up Stage 3: See changes, and begin to believe they are permanent, and perhaps test them a little Stage 4: Believe changes are permanent.
Part of it depends on your W too - I have had changes stick for 2 years, and W still refuses to believe them. Not because they aren't real, but because her self-constructed world comes crashing down if she faces the truth.
From what I read your W is asking to spend time with you - do it. This is apparently one of the bigger problems, and I assume you love and want to be with your wife - so go for it!
The thing that is a personal decision, and something you may need to investigate is if you're willing to tolerate the OM during these times. Sometimes a W will just want to "cake-eat" and have the best of both worlds, sometimes, there truly are feelings, and they are willing to drop OM.