Taking Our Own Family Pictures but Need Some New Ideas as What to Do?

My suggestion is to look at some professional photographers online portfolios for ideas. You will find a ton of exmaples of cool or interesting photo ideas that way.

And I have to say this, I hate when I ask a question on here, and a thoughtful responder decides to direct me to the internet to search for my answer, rather than actually answering my question with her thoughts/experiences/ideas... and I just did exactly that! LOL

But seriously, the reason I am directing you to professional photographer websites is that IS what I DO. LOL When I need ideas, I go looking for what the professionals are doing! There are just so many possibilities...

Have fun! I love photos!

not super helpful but, try black and white photos too that give a whole different feel to something you might have already done before.

If you need a laugh and what not to do I get a kick out of ackwardfamilyphotos.com super silly.

The best pictures I've taken have always been outside in the natural light. Try taking pictures of them playing in the backyard, especially if you have a swing set or pool. Give them a jar of bubbles and start shooting away.

OMG Thanks V.M. for reminding me of that site! I visit it every so often for a laugh.
S., I tend to rely on volume to get photos, so if you like an idea, play around a lot with it. One year for our Christmas Photo I propped the camera on a tall ladder outside, we were under our cherry tree with a gazillion yellow leaves on the ground (late fall in CA). I figure this might work with tree blossoms that fall off in the Srping. We ended up with a nice picture of the three of us (me, hubby, dd) and our two dogs. Even with the quantity of pictures I still used photoshop to pic the best of all of us to combine in one pic ;-). So it was unusual because of the angle, we were also kneeling with my daughter standing between us and it just worked really well. There is also a remote with our camera that comes in SO VERY HANDY. I also had propped up car shades in the tree out of site to reflect more (soft) light down on us. Let me know if you want to see the results. This was probably my one and only trick photography wise (not sure who I was channeling that day but they haven't been back since ;-).

I guess the answer really depends on what result you are looking for. I have some great captures of my kids just looking right at the camera. We also take our own photos so I can give you some ideas of what we have done. Some of my daughter just sniffing a flower (would be cool in black and white with a color flower), we have some great ones of the kids playing in the leaves, my daughter kissing my son on the cheek or vice versa, on a swing. Take your camera to the park and just take pictures, some posed and some unposed and see what you get. You may be surprised. Pictures of the kids blowing bubbles has to be my favorite, the faces are priceless and the bubble make for cool pictures. Action shots of the kids interacting together not looking at the camera, maybe reading a book together, or one helping the other to ride a bike or reach something. Catch a moment when they are full of giggles and just start snapping pictures. Planned pictures do not always work out for the best, just keep that camera on the ready and take random photos of them having fun, you might just capture something wonderful.

Outside? With a family pet?
Kind of depends on what they are into to.....
I do our own pics of our kids at Christmas time and for their Birthdays - which are both in the summer. I like pics of them at the beach, by the garden or in the grass.

Sometimes the "actual" background is not as important as the "feel" of the background--interesting old brick wall, stone building, interesting fence or gate, greenery at a park, etc.

I would look into a local park. You can use the play equipment as a background or even use it to make your kids the same height. We use our park for pictures all the time.

Since you live in KCK, I would suggest doing them at one of the many parks, for instance, Loose Park is Great in the summer, they have lots of variety with their roses and fountains and statues. The plaza is also a nice area, if you go when there are not a lot of people to mess up your shots. It is well known for its fountains. My daughter and I got some great shots at Crowne Center, in front of the fountain at Union Station. This time of year when the red buds and bradford pears will start bluming will be a great backdrop.