Usually in a situation like that I'll glue and micro-pin a 2" or 3" wide strip of 1/2" plywood filler around the outside perimeter of one of the mating surfaces, assuming your face frames protrude 1/4" proud of the cabinet side. Then you have an-inch-and-a-half thick solid screwing around the perimeter of the cabinets you can run 1 1/4" screws into from both sides.

If you can anchor 2x4 cleats to the floor, you can screw through the toekick area to secure the cabinets, then cover with trim.

If you have room, a washer head screw thru the MDF and into the face frame of adjacent cabinet? Be careful because you don't want the screw blowing out the face frame. Won't be fun; may not be possible.

The cabinets must be joined to each other properly. And you must account for the proper fillers for clearance in the design as well. Neither appears to be happening here. Joining is the easy part. When joined, it won’t work though.

Redesign, new cabinet sizes, and Pros.

Have you tried to open the drawers yet? It looks like you need a filler.

Drawer base against the wall has 5 inches of filler to the left ( between drawer base and peninsula) and I only needed 3. Also I’ll have 3’inches between between peninsula and corner for doors to open so they don’t hit the drawer base.

I can try to go through the mdf diagonally to the other face frame, but seems like there should be a bracket of some sort that I could use. Worried about tearing up the mdf and missing the face frame but this might be my only option

Corner cabinet will be anchored to the wall and I cannot use 2x4s under it to anchor to the floor, only the peninsula cabinet is anchored to the floor like this.

No one needs 5” of filler anywhere. That is just more bad design. But you have no filler between the backwards corner cabinet and wall. Or the peninsula cabinet and that corner cabinet. You haven’t accounted for the thickness of needed panels either. All of that has to be factored in to the math and clearances.

I should have made it clear I was speaking of only the peninsula cabinets--not the cabinets secured to the wall. I don't recall the exact thread, but I read once that cabinets should not be secured to both the wall, and floor cleats, due to settling/shifting of floor, which can put stress on the cabinet structure.

Sophie that has all been accounted for you just can’t see it in the picture. And the 5” filler is going to be shelving space. I had a flooring issue to deal with so 3” turned into 5”, that is how the design worked out in the end. Your negativity is unproductive. I appreciate most comments, but really looking for advice on connecting the 2 peninsula cabinets.

I like Joe's suggest of adding a cleat inside the cabinets. Just make sure that the position of the cleat doesn't interfere with drawer glides or shelves.

You are still not understanding. The cabinets should not connect at all in this scenario. There should be fillers in between them all. Or you would need to account for back panel thickness and pulling the corner cabinet a lot more than 1” off the wall. That corner cabinet can not join directly to the wall. It requires a filler. If you use the rear of the corner cabinet as the filler on the face run, it has to be paneled.

Sophie the skins and fillers are accounted for as you’ve commented, you can’t see it in the picture and skins haven’t been installed yet.

Joseph when you say hot set, do you just mean glue gun? And thanks for reminding me to make sure they don’t interfere with shelves, because I was thinking of one full length strip which obviously won’t work

If you’re joining cabinet to cabinet here, then you have not done the correct design with the correct fillers. Period.

I drew up a crude diagram here with my finger on my phone, but whatever, just live with not being able to open your doors properly.

Flip the corner cabinet and the peninsula cabinet upside down and glue/shim/screw them together below the bottom shelves. Then turn them right side up and cut out the top of the sides to accept a 1x2 on the flat behind the upper stiles and backs and glue/nail/screw as needed.