My advice don't get too hung up on any birth plan. They can change in an instant over the smallest of things.
I had planned to birth in a MLU with a pool, wound up having a planned c section. I never even got to experience contractions.
Signs of pre-eclampsia and a big baby - the medical advice was she needs to come out a week on x date. It was bizarre. Like turning up to a doctors appointment- not at all how I imagined!
Everything was fine but I'm glad I kept an open mind, while I didn't envision that happening - I tried to visual all the different scenarios I might end up in. I imagined being in an operating theatre, imagined birthing at home because I couldn't get to the hospital, imagined being in a pool etc etc. The only one I didn't imagine was that I'd need an appointment and it would be a planned c section. I imagined a dramatic c section with all alarms blaring.
A c section wasn't what I wanted at all but imaging myself in all the different scenarios really helped when I suddenly realised my options were narrowing over something beyond my control....
Personally, I'd go for MLU, because if something isn't going well, or you really need stronger pain relief - you're right there.
I think a home birth for a second baby is OK- once you've gone through it all and know what to expect.
P.s for my hospital you had to be within a certain radius of the hospital to be considered for a home birth, so before you get set on something make sure you're eligible purely from an address perspective.
Also to note - you can choose any hospital you want to birth in (within reason). Don't feel like you have to birth at the place nearest to you.
Of course, that's only my view - you're the Mama! So it's entirely up to you xx