iPad Remote / Home Sharing IP Address Doesn't Match

Each device on a LAN has its own IP address. If the software requires you to enter an IP address for the device with which you are creating a connection then it will be the IP address of that device. You can get a list of IP addresses by logging onto your Router. Of course at the time of making the connection both devices must be logged onto the LAN and visable to each other.

I think you have made a wrong assumption but I am happy to be corrected I am unaware that two seperate and distinct devices would share an IP address on a LAN. What you might have to do is log on to the Router and release the IP addresses for each device and have the router [an automatic process]re-allocate them. Dependant upon the configuration of your router the IP address in all likely hood will either start with 10 or a 192 number. My iPhone on the LAN for example is 10.1.1.6 and the iPad 10.1.1.8 and the Mac 10.1.1.10

in order for the home sharing to work both devices must be on the same IP

This is incorrect. They must be on the same LAN (Local Area Network). If they are the same IP address, it will mess up the LAN and nothing will work.

I will happily admit to IP's and that sort of thing being a bit outside of my level of comprehension

An IP address is simply a specific, unique address for a device (such as 208.16.231.12)

Any advice on how I can get these devices to share the same DHCP?

DHCP is *Dynamic Host Configuration Protocol*. This is how IP addresses are issued to devices wanting to connect on the LAN.
In this case the router will dole out an IP address to each device connecting to the LAN and keeps track of who is who.

As long as the devices are connecting to the same router, everything should work fine.

I am trying to set up home sharing on my iPad and iMac

You can't Home Share to your iPad.
If you are using Remote on you iPad, you can use your iPad to control iTunes on your iMac which can in turn be home shared with another computer.
You can't stream or transfer songs (using iTunes Home Sharing) to your iPad.

Do you have wifi enabled on the iPad?
Are you connected to the same wifi network as the AppleTV and iMac?

how are you supposed to set up Home Sharing (which requires the same IP address

They do not require (and cannot have) the same IP Address.
Where you seeing this?

The 2nd pix you posted is what you would see if there were other iTunes libraries Home Shared on yoru lonetwork.
Do you have a 1st gen AppleTV with iTunes library on it? Or another computer with Home Sharing enabled?
If not, there's nothing to *Home Share* from so you won't see it on your iMac.

See this page -> Remote app for iPhone, iPad, or iPod touch can't connect to iTunes or Apple TV

My understanding is that 'my current location' used by an application installed on a iPhone/iPad is based on the triangulation of 3G Transmitters assisted by GPS. So if you have 3G and Location Services aka GPS disabled then my guess is it won't work.
There is also an assumption that you are also subscribed to a iPhone Data Plan rather than just a Mobile Phone Plan. In this part of the world iPad users with 3G and Wi-Fi can subscribe to a 3G Data Plan on its own.

Also in this part of the world my guess is that most iPhone users may be on what we a Cap Plan which includes a number of Phone Calls at an agreed value plus SMS plus MMS plus data for a fix monthly amount. You need to check with your ISP if you have a data plan what your monthly allowance is and how much you have currently used before the next billing cycle.

'my current location' used by an application installed on a iPhone/iPad is based on the triangulation of 3G Transmitters assisted by GPS

actually, it's the other way around. Assisted gps means it gets location data from cell towers first which helps speed up getting the gps coordinates.
And if the iPad is not 3G with gps, it uses the coordinates of the router (based on Skyhook data) to get location data.
There's no need for a 3G signal to get location data.