Can you share a photo of the plumbing under the sink? I'm not a professional, but I do play one on the weekends (not really, but I have done quite a bit of DIY).

Why do you want to eliminate the pony wall? Is it an aesthetic reason? Or do you want to change the layout of the kitchen and the wall is in the way?

My assumption would be that your water and waste pipes run from the exterior wall into the pony wall, along the pony wall to your sink cabinet and then make a sharp 90 turn into your sink cabinet. Another possibility is that your plumbing runs under the floor to your sink and not through the pony wall (or under the floor and up the pony wall and then into your sink cabinet). Basically if the plumbing does run all the way through the wall, you'll have to re-route somehow. Either you have to route it under the floor or through all of the new cabinets instead of the pony wall if you eliminate it. The latter is obviously not desirable. You could also consider moving the sink in your layout if that means a better route for the plumbing.

I also notice that you have electrical in that wall, so you'll have to figure out what to do with that as well.

We had the same situation, down to the same awful tile, and removed the pony wall, replacing it with 12" deep end cabinets and center display shelves. It was all custom made. I don't think you can bump it out further because of the door. We were able to add a 14" trash cabinet to the peninsula by using a smaller sink base and going 5" into our hallway, even with the short wall near the fridge. We changed from a double sink to a deep 23" single to accomplish that. I love the one level peninsula.

What kind of countertop are you planning to have and will there be an overhang for seating?

Why not cut the wall down, pull the drywall off and have it finished with panels and trim matching the cabinets..

If you're on a crawl space, then it shouldn't be too difficult to move the plumbing into the sink base.

If you're on a slab, you could have the run of cabinets made deeper, so that with the wall removed, all the plumbing would be in the cabinets.

The electrical should be able to be moved into the cabinets. So it's not a big deal.

You're right next to a sliding glass door. If you're talking about moving these base cabinets over one foot, you may not have to move the plumbing at all, just pop the new cabinet over the existing pipes.

Even on slab you can often just run the pipes in the toekick area. That's what all my neighbors here have done when renovating a similar configuration.

Here is a picture of underneath the sink. We are on concrete slab. We do not want that bar height overhang, or any overhang at all because that limits how far out the base cabinets can move outward due to the slider. I'm short and it's hard to see over it to watch my very young children playing. We want it level.

The width of the kitchen is only 45". It's very cramped. We want to move the new cabinets outward as far as possible to give us more room. The sliding glass door obviously limits how far we can go, so complete removal of the wall and figuring out somewhere the plumbing can go would give us the most room to work with. It's 10" from slider to wall plus 6.75" of wall. A width increase of 16" in our kitchen would be very significant.

I appreciate all the thoughts so far, and that picture was excellent. Thanks!

"Can I remove the wall and somehow have just new cabinet backs facing the family room?"

Yes. You'll install a finished panel.

"How does the plumbing enter the new cabinets?"

Through the sides and/or bottom of the new cabinets.

Check with your division of inspection first, please.

Our plumbing enters from the wall through the side of the sink cabinet. Our sink cabinet is open from the sink to the wall, creating a void in the corner. The 12" cabinets are butted up to the back of the sink cabinet and DW. I can take a photo of the guts for you this afternoon.

I know this

is 4 years later but, wh what did you end up doing with that wall? My project looks just like that and i want to take it out completely and move it to the wall under the window