How do I keep my Mini Dachshunds from getting between the deck rails?

Try putting up some chicken wire or something like that. You can just staple it too the deck rails.

Sounds like your deck rails are no longer code compliant. Next time you have to rebuild or refurbish, check your local code first. In the interim, I would go with a paint or stain lattice to coordinate with the current structure.

https://www.decks.com/how-to/373/deck-railing-codes

https://homeguides.sfgate.com/us-building-codes-deck-railing-61979.html

Hello. We don't have a deck but we do have a wooden picket fence in the back yard. I have two mini dachshunds myself. The eldest is too fat to fit through the fence, however my one year old can squeeze right through if she tried. Also our neighbor that lives directly behind us has a one year old male dachshund that was bought from the same breeder but a different litter and my youngest loves him to pieces. There is a small ditch that separates our houses. They allow their dog to run free if their out with him. So he comes to play with my dog. Even when he's not outside, she runs to the back fence in hopes of seeing him...so cute! Because of this my husband did put the chicken wire maybe 1/4 th of the way up. It's not that noticeable. I wish he would've put it up a little higher though. She has put half her body over top of the wire through the fence trying to get to him. Hopefully he will be adding more wire...at least in the area she tries to get through.

Are your dogs jumpers? I never would have thought they could jump as high as my young one does. She's so full of energy and you would think she's a billygoat instead of a dog the way she jumps. (And i know i really need to somehow stop her from the jumping being this breed is at such a high risk for back injuries).

Chicken wire

I had a similar problem keeping a kitty on the porch without any visible barrier, like a screen, because of community rules. I found that tightly stretching deer netting from post to post was strong enough to deter getting through porch vertical slates AND was totally invisible to my neighbors! I used the transparent zip traps to secure the netting. I could also pull it higher than the top railing to prevent successful jumping. In apartment buildings, you would need to be on the second floor to be invisible. Deer netting was from Lowes.

thin transparent zip straps! not traps. :-)