Being tired can take all the libido and desire out of a woman.  If she's tired all the time, she'll be passion free.  You can turn that around.

If you want to increase your wife's libido, then let her batteries recharge.  Offer to take care of the kids one weekend day for a couple of hours so she can take a nice long nap.  If you can, after the two hours is up, take the kids to a sitter or set them up with a movie and tell them not to disturb you until it's over because you're taking a nap, too.

If she's still sleeping, gently wake your wife with a light massage.  Just massage her shoulders and neck.  When she's awake, ask her if she wants you to continue.  Move on to her feet, calves and then thighs.  Here's where she'll let you know if she's in the mood.  Watch for body movements that may be an invitation, but don't have expectations.  You may just barely brush by certain areas and see her reaction.  Don't rush it and don't be obvious - don't put any pressure on her.  If you think she's indicating she wants more but you're unsure, be polite and ask "do you want me to go further?" 

Always check in - because you do not expect sex - by asking "does this feel good?  Let me know if I do anything you don't want or that doesn't feel good.  It's ok."

This will take the pressure off and relax her.  Then you just take it slow and enjoy your wife.  If the kids are home, the chances of anything more happening are about 10% - they will likely interrupt.  But the massage will stay on her mind for a while.  Take your unused energy and build a new addition to the house or something.  Or just be patient - your time will come.

If the kids are not home, be happy if she is turned on and keep up the same slow romantic pace, but do not make a fuss if she doesn't - when you're done, be kind and gracefully leave to go get the kids. Remember: you're doing this for her - to rekindle her passion - to charge up her long term libido - so be in it for the long haul.