I have a Canon Ixus 430 (2004).
For North Americans, this would be a Canon ELPH S410 or S500. :)
Is there any way I can force the normal flash to flash even in very sunny weather (in manual mode)?
Yes. On page 58 of the user manual there is a Flash on setting in the camera menus that will force the flash to fire with every shot. And this is only available in "Manual mode".
However, what the camera/manual refers to as "manual mode" is similar to the "P" (programmable auto) mode on higher-end Canon cameras. I tend to say that for "serious" photography the three features I want in a camera are "PSAM" modes (with Canon, that means M/Av/Tv/P modes on the dial), RAW capability, and maybe a flash hotshoe. The Ixus/Elph models tend not to have these things; the S/G/G#X Powershots do.
Given that you're using a 4MP 2004 consumer camera, it's not surprising you're having problems with shooting in low-light. The older sensor tech, maximum ISO setting of 400, and lack of controls are all against you when it comes to low light. I think possibly your only option is to use the camera on a tripod with the flash... or consider saving up for a newer camera. :) The used market in P&S cameras has gotten pretty good given the recent advances in smartphone cameras, and you could probably pick up, say, a 2012 12MP Powershot S110 (which does f/2, RAW, and has PSAM modes and can do iso 1600 pretty well and can be set to iso 6400) for less than US$100.