Never leave the chores undone at night. This helps me so much! Wrap up the day's chores before bed. Start the dishwasher, put away laundry, and tidy the house before bed. This way you are starting the morning fresh and not in a chores deficit.
The five-minute tidy-up
If you have to be the one doing all of the tidying up then your time will be consumed with that all day instead of playing with your kids. Introduce the whole family to the "5 minute tidy". This is based on the idea that many hands make light work. As the house gets out of order during the day or evening, simply say, "It's time for a 5-minute tidy!" Set a timer and tell them that everyone has 5 minutes to get the house as tidy as possible. Now everyone, including mom and dad, set off to do a quick clean-up. It's pretty amazing how a half-hour of work for mom or dad, turns into 5 minutes of work for a whole family and teaches kids to be part of the team. You can even give everyone a little reward for a job well done.
Own fewer toys
If you want to spend more time playing and learning and less time cleaning, own less! Kids are happy with a lot fewer toys than you think. They don't want to spend all of their time cleaning up their toys, so make it simple and own less. You will be surprised at how much more fun you will have. Read more about this HERE.
Time for yourself
The only way that you can spend more time full-engaged as a parent is if you are also giving yourself time alone, time with your spouse, and time with friends. Be intentional about doing these things...otherwise, you may lose your sanity. Cut out some time each day, either at night, in the morning, or during nap, when you can have a bit of respite. The kids need this too, so I always encourage blocking out some time for quiet or independent play for them as well. It's just good for the soul.
Do not overload your plate. We are all guilty of this and sometimes it can not be helped. But, having a packed schedule can hinder the freedom to just be. To play and explore and be spontaneous. Try to only tackle one or two things on your to-do list a day, if possible, and leave a few days a week free from extra-curricular activities or engagements. This may get harder as your kids get older, but setting some limits in order to have more downtime will save some sanity.
Enjoy your kids
The whole point of simplifying in order to parent, is so that you can actually enjoy your kids. When you don't have a million other things on your to-do list, you can have a lot more fun with them.