Not a mom (sorry), but I work full-time and often have people including children staying in our home (currently 2 college students), and I have two big fur kids (dogs).
Most important thing for me with GTD has been capturing everything. Particularly at home you have these moments - walking past the garage and thinking "boy, that gutter needs to be replaced." Walking laundry down to the washing machine and thinking "I need to buy xyz at the store next time I go." Your child mentions a special band practice next week. WRITE IT DOWN. Often you're all over the place when you're working in the home, so make sure you have a notebook and pen in your pocket with you all the time. Do weekly reviews to keep from getting overwhelmed with paperwork and projects.
Secondly, and this is NOT strictly GTD but more Flylady, I have created a list of morning, after-work, and nighttime routines, and weekly, monthly, quarterly, and yearly things that need to get done. Every night I take time (usually just 5 minutes) to read through my routine lists and create a checklist for the next day. I just started doing this about a week ago and it's working great - before, I had my routines written down, but I'd forget to do the once a month/quarter/year stuff, so the daily checklist prevents that.
Every time I do something that is not on one of these lists, I think about how often it needs to get done and then it goes on the list. For example, yesterday I noticed that the baseboards were filthy, so I cleaned them and then wrote it down on the quarterly list. If you do want to do the strict GTD implementation, you would put an index card in your tickler file and move it to another month or day every time you complete the task. But I like having all my chores written down in one place, and I can hand my list to someone (husband koff koff) if I can't do it for some reason.
I know it isn't strictly GTD to do things because it's Monday, but with housework, if you do things on a schedule it often saves time and money in the long run because it prevents disaster cleaning and repair.