Translation:This is the farm that we cultivated last year!
No, kwamba would be incorrect.
Kwamba is a complementiser, not a relative pronoun. It does not introduce a relative clause but instead introduces a complement clause.
In the sentence "I know that this is the farm that we cultivated," the first that would be kwamba. The second that would be ambalo or just -lo- within the verb.
I'm 99% sure this sentence should be Hili ndilo shamba tulilima ... or Hili ndilo shamba ambalo tulilima ... I think tulililima is a typo.
I'd appreciate feedback on this point from someone who knows better, but in any case, I know the difference between kwamba and the amba- words so let me know of you'd like more explanation on that. I'm a grammar nerd and I can go a bit deeper into that.
So do they mean tulilolima instead of tulililima? Is that what you mean by "just -lo- within the verb"?
-lo- is the relative infix for singular nouns of the ji/ma class, like "shamba". I cannot confirm that this leads to tulilolima, because I am missing the object infix -li- then.
Actually, I would consider two possibilities for "the farm (that, which) we cultivated":
relative included in the verb, can be done for na, li and ta tenses only
shamba tulilolilima (tu-li-lo-li-lima- _ )
relative expressed with amba-
shamba ambalo tulililima (tu-li- _ -li-lima- _ )
My two examples look similar to the current Kiswahili solution, I just used in addition the relative. So it seems possible, that the relative could be skipped in Kiswahili sentences, too, at least if the verb contains an object infix?
I am happy about any correction or confirmation by others.
Isn't the second "li" an object affix referring to "shamba"? But, I don't think it is really necessary and that "lo" should be in there for the relative clause