It depends on how sound proof you want the room. Don't go overboard or YOU won't hear if there's a problem.
Firstly make sure both rooms are carpetted including underlay, most noise travels via flooring.
Secondly what doors have you got...go for solid wood if you haven't got them already.
Make sure the beds are not placed against the adjoining wall.
If you've done all this you're on to the more intrusive and expensive solutions. There are a few choices here: -rebuild and insulate the wall, -add a new stud wall ontop of the existing wall (with more insualtion), -you can buy a soundproof board that you place over the existing wall too, although this is very expensive, -you can also try carpetting the wall (or using a thick heavy curatin to bounce the sound back) although this isn't ideal.
The only thing I'd say about blindly injecting stuff into walls is that you don't know what's in there. Bared wires etc. I've never heard of any foam injection specifiaclly designed for sound proofing although theoretically expanding foam filler would do the job...but like I said I personally wouldn't do that without know the exact condition and sleeving of the electrics or any pipework that may be in there and the exact volume of each segment of studwork etc, etc.
I can check with our builders tomorrow if you like? They're just doing ours and they have some solid looking green insultation stuff that comes in thick sheets that they saw in to blocks and then put that between the two plaster boards of the adjoining wall.
What is your house constructed from? I ask because we looked into soundproofing and discovered that it is ineffective in houses with breeze block walls.You can test this by going into a room on the other side of the house and making a noise.If another person in the room you have the problem in can hear the noise,soundproofing won't help,as the sound travels around the internal 4 walls of the house.
Our problem was our elderly neighbour's loud tv.After reading up on soundproofing I stood in the furthest away room of our house and put my ear against the furthest wall.I could hear the tv just as clearly as I could at the party wall.
If it is any consolation,they will probably get used to the noise and sleep through it-we rarely hear next door now.