Check my sentences using the word "nonetheless".

That one is fine.
2) I gave her my Ipad, nonetheless she kept being rude with to me.
3) They didn't like the service, nonetheless they decided to be kind with to the workers.

Thank you! :)

Your use of "nonetheless" is fine in the last two as well, though the word would usually be at the start of a subordinate clause. I therefore recommend adding a comma before it, just as you did in the first sentence.

When you are acting toward someone, you always say "to {them}", not "with them"; "kind to", "rude to", "pleasant to", etcetera. You would use "with" if there is some kind of interaction between the two people, rather than one person acting solely toward another. For example, "He was affectionate with his wife".

(You can also change "nonetheless" to "however" in these sentences!)