I agree with FA, it's way too soon to for you guys to be getting this domestic. Unfortunately, this is something that happens a lot when couples "bring in" a "third" (usually a girlfriend). They kind of just forget about the whole dating thing, and try to insert him/her into their daily routine like a missing piece of their puzzle. Which is, of course, going to feel weird, for many reasons.
First, you all need to find a way to see each other without the kids. If you were single, would you take your child on your initial dates? No. Neither would they. Usually, even single, mono people do not introduce their dating partners to their children for quite some time. A poly relationship is no different.
Second, there should be no expectation of you spending your time together at their home, doing their stuff, on their routine. When I was wiling to date couples, I had a couple that did that: "oh, just come over and stay the weekend. This is how we make coffee. This is how we make the bed. This is what we listen to in the morning while we get ready. This is what we..." And on and on. The problem was, it was all about them--totally couple-centric--and I was just expected to insert myself in whatever space they decided I should fit. For me to do anything a different way, I had to make a big deal of it, which was very uncomfortable. This is, unfortunately, very common with couples. So, you're not alone in feeling out of place, and it's very likely to continue as long as you are dating an established couple and doing it all in their established space.
If you decide to keep the relationship up, you need to date like you would normally date. Get babysitters for the weekend, and get a hotel, go camping, etc. There is no difference in mono and poly dating in terms of speed at which things should happen. If you were dating a single person with kids, it's unlikely you'd already be spending weekends being all domestic at this stage--there's no reason to do so just because there's more people involved. You wouldn't likely be doing yard or housework with them already, etc.
Also, you should ALL read
So Someone Called You a Unicorn Hunter. It may help you verbalize what your feelings are about certain situations, and it may help them see what the pitfalls and dangers are, and how to help mitigate them.