I have some solutions to the “need an heir to the throne”, firstly ask the princess for a night of fun to make a baby.
If she agrees to baby and touching reluctantly (she didn’t want to before):
plan a night with the princess to do so a month later from the date (ex of plausible excuse: “I want it to take on our first try, so I’m going to research everything in the library and line up my cycle to make sure the baby turns out healthy the first time. It’ll also give us both time to get our bodies ready and in prime condition, which can increase our chances for a boy already, with the added benefit of never having to do this again.”), for that entire month ‘walking around and reading books for research outside since he can focus better outdoors’, go off alone with knight bf and get bred over and over, once the month is up (which prince should very much be knocked up with a little knight by now), get it on with the princess, carry the baby, and have an heir that’s also knights kid, plus it won’t be suspicious since a lot of babies can be born a month early (if it even is born on time, most are late anyways).
If she agrees to a baby, but still not wanting to touch the prince:
Plan on having the princess fill something (ex: piping bag) with her baby batter (when she is able to nab something, or prince takes his time getting it), do the steps for getting bred by knight bf that were in the previous plan, and once princess gives him the baby batter filled thing, pretend to have filled himself with her jizz, and have an heir that’s the knights baby without it being suspicious (or do the month thing from previous plan, just with using the jizz filled object instead of fucking).
If she doesn’t agree to either:
either hope shit doesn’t hit the fan without an heir, or hope she at least agrees to help fake pregnancy and adopt in secret.