Ooooh, I can see problems AngryBeaver.
OK- I don't know rabbits. I've never kept a rabbit. And from what I've read on here, I don't think I'd ever want a rabbit.
But I love my guineas and I've had them from 9 yo - 22 yo. Then more recently my DD got the boars.
You've kept bunnies before but have you kept guinea-pigs?
I know FernieB has a rabbit and 2 guinea-pigs but I don't know how much contact they have (they seem to play together and the rabbit seems very tolerant of the pigs).
Maybe put out a shout to her for advice.
But every website from the GP sites to the RSPCA says GP and rabbits don't mix.
Rabbits aren't really considered suitable for young children (I know you said your previous rabbit was placid but they're all different) They can kick and bite . And some don't like being lifted.
Your little guinea is scared understandably- but they are prey animals. Their instict is Hide.
My bigger boar gives the most unholy shriek when he's lifted (he did this the day we met him, so it's just him). It's just his protest. He's fine when we catch him.
Some posters corall their rabbits into a cat carrier.
I'd say you should lift the GP, wrap him in a towel and let your DD cuddle him.
Rabbits/Guineas have different food needs.
Pigs need VitC rich pelllets -unlimited.
Hay, veg.
Rabbits pellets are different, and they need less. Less veg. Unlimited hay /grass
Rabbits can give guineas a respiratory infection.
They don't communicate the same, it'd be like me living with someone who only spoke Italian.
And a rabbit can bully a GP and kick it to death (those feet are powerful, as you know)
Where did you get them from? Did they advice it to be ok?
If you want the rabbit then get another rabbit (opposite sex and neuter both)
If you want the guinea- depends what sex the GP is. Female+ female.
Male+ male (but it can be difficult to pair boars)
Or if it's a boar, neuter (risks involved) and get a female.
In your shoes I'd seperate them and try and rehome one.
(Of course I'd keep the guinea-pig but I'm biased) 
Good Luck.