Got a little complicated whilst writing this - 1 refers to your modem, 2 refers to your wireless router.
This is one thing I hate doing as it can change based on device manufacturer and features. Personally, if you can upgrade 1 and 2 and just have one device, you will be better off.
For a start, if your 2 actually supports this e.g. has an Ethernet WAN port instead of a smaller telephone line adapter, you may not even have to disable DHCP anywhere - simply make sure the 1 works (connect it up to one pc) and if it does, plug it in to to the 2, and then it should "just work" - if it doesn't, your 1 is more likely to be an actual router (just with one port).
so, if 1 is actually a router instead of a modem, I would recommend that you see if you can change the mode of 2 and basically disable all routing and change it to an
access point, this will then do all the DHCP and everything else at 1 whilst just providing an access point to wired and wireless devices - by far the best way. (After changing this, you may have to first manually set the ip of 2, this will mean that all devices are pingable and accessible on your network and the easiest to manage.