Which tirthankar should we not have at home temple
In Jainism there isn’t a universal rule that says you must not keep the image or idol of any particular Tirthankar in a home temple. All 24 Tirthankaras are revered, and homes often have idols or images of multiple Tirthankaras with proper devotion and respect.
If your family follows a specific tradition (Digambar or Shwetambar) or a local guru’s guidance, there may be particular customs or preferences for which Tirthankaras to emphasize or how to arrange the shrines. In that case, it’s best to follow your guru's instructions.
If you’d like, I can check for a page on JainKnowledge.com that describes home puja practices or the role of Tirthankara idols in a home temple.