The good news if you have identified all the red flags before you married this man, so you can still opt out.  Love is never enough.

So he brings his kids to your home so you can cover the costs AND do his job of parenting? HELL NO!

This is your home and you have every right to tell them to keep out of your pantry and fridge, that all drinks other than tapwater are off limits. Tell them to clean up after themselves! If your partner isn't happy about things he can take them elsewhere. You know what? Save yourself a lot of trouble and tell him to keep them somewhere else on his visitation time because, after all, visitation is for them to spend time with their father, not to be babysat by dad's girlfriend, right? Imagine how relaxing those weekends could be ...

I won't address the behavior issues but its time for Disney Dad to pony up much more $.   Groceries, replacement, extra cleaning, etc.

Have you ever bluntly told him... "you say you will parent these kids.. you don't.. you say you will replace or repay me.. you don't.. why should I believe anything you say when actions never meet words"

I personally would cut someone off that is using me like this.. and that is clearly what he is doing.

Re-read your original post above with the perspective of providing advice to the person who wrote it.

Then do that.

Which is not unclear nor is it complicated. Purge this user and his failed family baggage from your life and the life of your young daugther.

Please.

And do it now.

Just leave all day on the weekends and buy groceries after they leave.  This way (since he pretends not to understand your desires for a peaceful home) he is now forced to provide entertainment and meals for them. Charge him $xxx amount for a weekly cleaning crew to come through after they leave each weekend.
 

Sometimes people have to learn the hard way. 
 

Also based on your post it sounds like you let him move in to your home and import his kids. 
 

Firstly, in the future never allow men to move in to your home (especially if theyre bringing a crew of people/dependents with them too). If things go south instead of walking away your tenant has rights and could end up a squatter nightmare. 
 

If you chose to ignore this tip then it's imperative to discuss on the front end the expectations of said living arrangements in order to preserve your peace and sanity in your home. 

Stop with I will replace it.  Tell him he is going to buy it before, not after. Try to figure out how much food/ materials/ internet. His kids use.  8 days a month. 30 days in a month. 1/5 of the month  20%.  As get a additional 20% on internet. He pays 60 % of internet you 40%   
Set up rules for the house. Who clogs the toilet unclogged it and cleans up    Every family member has a Job including your bio DD. 

Does your fiancé live with you? Your post wasn't clear. CIf he doesn't then I would suggest he keeps is kids at his place when he has  them. If you want to spend time with him you can go over for dinner or whatever but these (nearly) adult kids don't need to be staying in your house every other weekend if he has a place of his own. 

He is raising his kids on junk food, cigarettes and uses screens as a replacement for parenting? AND he expects you to cook and clean for them while they're desecrating your home, your safest place in the whole world? He's looking for a wife appliance, not for a partner to love. You need someone who'll slay dragons for you. 

I always tell young people "the best you're partner will ever treat you is in the first year if your relationship . It won't necessarily get worse, but it 100% won't get better".