I have one that has worked great for both my girls. It secures to the seat well. It basically snaps on. https://a.co/d/bYk5geU
We have one that has suction cups and it folds up, so we have one that stays on our toilet and one that we take with us. The one we had that "clips" in the toilet didn't fit, but this one works great no matter the size of the toilet seat!
https://www.amazon.com/Folding-Travel-Toilets-Non-Slip-Suction/dp/B07MTRHDXZ/ref=mp_s_a_1_1_sspa?crid=2F85EERDSHOMG&dib=eyJ2IjoiMSJ9.tlHqCROH-QqGDbUu4uxKO3en2BslxAPGAzVF7HbcbYHMcVgipV_ZeFAK8tBh7y5oY_6V23tUu1eTBIF7DZrUl_yUVksKYseTi__z8YWEm7Ms1rdOs1gQZE3hdJwU3HgSEHPsR41Nl2nDj08p7lmLeZCG1HxjLNp1_AGGKI8e8NyI1eVBdi_mcvhhD5jrjOmtmvC-ILnTNA5FaYMOrlgmYQ.j8qxlOlnYngulIeX3YKAGDcE_trE4IzEBaCuqEU2g3A&dib_tag=se&keywords=toilet+seat+with+toddler+seat&qid=1742130388&sprefix=toilet+se%2Caps%2C139&sr=8-1-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9waG9uZV9zZWFyY2hfYXRm&psc=1
If nothing else, is it possible to get a different seat? We ordered one off Amazon that goes on like a regular seat but has a second toddler sized one that flips down. I get not wanting to replace what's there but you can always save the original seat and put it back on if/when you move.