I think you've got two different issues involved here:
- How to use LINE/LOAD of a GFCI - e.g., connecting neutral to lights or disposal from LINE and connecting it back to LOAD will create an imbalance so that as soon as you turn on the lights or disposal, the GFCI is guaranteed to trip.
- Colors of wires vs. function - e.g., connecting a white from a switch (which is really either hot or switched hot) to LOAD neutral will cause a dead short when you turn on the switch.
Kind of hard to determine everything here. Pictures would help. But here are some things to consider:
LINE vs. LOAD
With a traditional receptacle (as you had originally), there are two hot screws on one side and two neutral screws on the other side and you can use each pair to daisy-chain to other stuff (lights, disposal).
With a GFCI, one side is LINE (incoming) hot and neutral and the other side is LOAD (outgoing) hot and neutral, and never the twain shall meet. The GFCI protects the receptacle itself and anything/everything on LOAD.
Note that generally speaking (there are some exceptions for certain bathroom lighting over a tub or shower) you do not want to put lights onto a GFCI protected circuit as a trip on that circuit would also turn out the lights. For example, if you are working in the kitchen and the receptacle has a food processor with nice sharp blades and while running it trips the GFCI, you do not want the only kitchen lights to go out at the same time. On the other hand, while disposals e not required GFCI protection as long as receptacles have, there is some real logic to protecting a disposal, which is turned on when you are running water through the sink and your hands are wet, etc.
Given all of that, the basic configuration here should be:
- Incoming power (hot and neutral) connects to both the LINE side of the GFCI/receptacle and the lights.
- Outgoing power (hot and neutral) comes from the LOAD side of the GFCI/receptacle and goes to the disposal and the peninsula receptacles.
Based on the description, I think you are in (typical) cable land rather than conduit land. In which case:
- Incoming power = black hot/white neutral. These go to the hot and neutral screws on the GFCI/receptacle LINE side.
- Peninsula recptracles = black hot/white neutral - GFCI/receptacle LOAD side.
- Lights = GFCI/receptacle LINE side, see below
- Disposal = GFCI/receptacle LOAD side, see below
There are three possible ways that the lights and disposal could be connected. (Plus others that are not correct.) Impossible to determine which one you have without pictures or additional details. Lights and disposal may have different configurations!
If a switched item (disposal or lights) has the switch in the same box as the power source then you will normally have one screw (doesn't matter which for a "dumb" switch) connected to incoming hot and one screw connected to the switched hot going to the switched item. The neutral for the switched item does not connect to the switch but connects to the incoming neutral. In this case, the switch will have two black wires (in cable land). You connect the switched item's neutral only to the LINE (lights) or LOAD (disposal) side. You connect the hot screw of the switch only to the LINE (lights) or LOAD (disposal) side. You leave the switched hot wire on the switch as-is.
- Cable/wires going to switched item's box or to another box that contains the switch (with cable/wires going from the switch to the switched item and not coming back to this box).
In this case, the switch is elsewhere (not in the box you are working on) and you treat the cable/wires as if they were going to an always-on device (like the peninsula receptacles). Black hot to LINE (lights) or LOAD (disposal). White neutral to LINE (lights) or LOAD (disposal). Easy.
- Cable/wires going to switch in another box and to the switched item.
This gets confusing because the switch wires go in and out. In conduit land it is a little simpler because neutrals will always be white (or gray) hots and switched hots will always be other colors (black, red, blue, yellow, etc.) But in cable land you will likely have two cables:
If this is the case, the original setup would have had:
- switch white connected to incoming main power black
- switch black connected to outgoing switched item black
- outgoing switched item white connected to incoming main power white
If so, the new configuration will be:
- switch white connected to LINE (lights) or LOAD (disposal) hot
- switch black connected to outgoing switched item black (same as before)
- outgoing switched item white connected to LINE (lights) or LOAD (disposal) neutral
The best way to work on this is to connect only incoming hot/neutral to LINE. Test the GFCI/receptacle (able to power plugged in devices, TEST button turns off devices, RESET turns devices back on, etc.). Then connect lights to the LINE side and make sure they work properly (switch on/off, no effect from TEST on GFCI). Then connect the peninsula receptacles to the LOAD side and make sure they work properly (should power off/on with TEST/RESET same as the GFCI/receptacle). And finally the disposal (LOAD side).
Most GFCI/receptacles should allow two wires under each screw (screw clamp). Any place where you have more than two wires you will need to use a pigtail and wire nut.