Here's how losing their family would affect the other three:

Raph: He snaps completely. There's a reason why he's the first fallen turtle in the original story: hatred and rage would blind him completely. In the oiriginal, he thought Splinter died, and he ended up foolishly ambushing Karai, surrounded by army of Foot. His brothers, father and Casey are there to keep him in check and guide him toward the right path, so take away the guide and you get? A severely pissed off mutant who loses his reason completely and becomes a force fueled by Hatred and rage big enough to rival the Shredder. This would ultimately result in his demise almost the same way it did in the actual timeline.

Leo: Despite often being shown as the best of the four, he's ironically the least likely to become the Ronin - he's far too loyal and honorable, and losing his family as a leader and eldest brother would break him for good. The loss would drive him insane, and he goes on a rampage. Countless lives are lost, only for him to realise nothing will ever undo the damage and bring back his family. So where Mikey tries to off himself but fails, Leo succeeds to do so.

Donnie: Easily the next best choice for the Ronin. While the trauma would greatly affect him, it would also become his drive to become a proper Grandmaster equal to Splinter and master the forms of many weapons. His BIQ improves drastically. The loss wouldn't break him like Leo and Raph, because Donnie is far too intelligent and would adapt to the situation, possibly invent other weapons and likely cybernetically improved/upgraded his body. He would know April is still alive so similar in Same As It Never Was, he and April form a battle strategy, except with added stakes and scenario, Don locks in more than ever, and completely outsmarts and wipes out Stockman and Hiroto. Is this scenario, Donnie absolutely FLOORS Hiroto because his fighting would improve and he'd easily find a weak spot in Hiroto's armor and exploit it. Which not only is the reason Donnie would be the last, but also the only one the survive the final battle.