Who should I replace with Kate?

Kate is a good princess. Use her along with others until you get Sakurako. Next one is Sophia, Maria and Fathima. Finish quickly, probably within 55 rounds to get all three in the same conquest. France 98 is fun and great for that.

Also, you can remove Weyrother and Dumoriez and replace them with Sophia and Maria/Fathima.

Not so easy to plan your roaster.

First thing: the last slot is only for (temporary) trainer - a four slot game means a 3 generals lineup - not four ! Untill you finish the game with a 'last slot choice', long after the campaign

When you buy later a trainer for slot 4 - your to-be-trained general must already be in your HQ.
For example, you have already Dumoirez and Arnold - but not the general where you you want to regroup them in, so practical you have only One! slot for either Kate, Marmot or Weyrother.

I never noticed Weyrother, so I want to see him, after 40+ lotteries in the academy with a mod, I contolled that he is really Tier I. 5 refreshes later I found him. Just as a reminder: it is not extraordinary unusual that you wait 20 or more refreshes untill one desired general shows up (Diez).
Nothing more to tell about Weyrother. So the question is, Kate or Marmot?

My advice:
Do a French 1798 conquest. Keep a save of round 12-15 and one of 25-28 - block this 2 save!, and play the conquest, like you think.
After your first finish, you see on wich fronts your strategy needs more effort - ususlly one creepy undervalued edge of the map, and evreyone else is finished.
Now, finish up your conquest from your R25-save, with this knowledge.
After you finished the conquest, with 9999 💰+🍖 (always !- see my posts), we see wich princess you got, and plan your roaster.

Note:
R45,R55,R65 and R75 are targets, one round later you loose many years! finishing in R66 is a fail! R65 (better R55 or R45) you must get. For asian years, these breaks are after R30, R40, R50? (somewhere there you loose the chance to challenge Asia)

With Arnold you should invest in items. Items are much more important than additional ⭐. You can buy with Arnold in the campaign, what you want - and you can sell these items anytime you need medals, and buy them later again and again (renting items). Items are more important (and cheaper) than trainer.

PS:
Sophia is a as decent as cavalary general, as she is on artillery - She has only ½⭐ (+3DMG - Balistics) more competence on artillery than on cavalary with the same skills active - if you need a student for Dumo...