amount of money you put into diplomacy relevent
Money has nothing to do with how you can convince Great Britain and France to join. This is in another game

Foreign Entry is mostly influenced by the side who appears to be winning, estimated in-game by checking who has the higher morale (National Morale being mostly influenced by victories/defeats or the capture of objectives cities like the capitals, Vicksburg, Atlanta, etc.). Each turn, the side with the highest level move one tick toward him the Entry (from -100 to +100).
Then you have several options (4 on each side, but they do not appears all at start), where you can bid with a % chance of success Morale Points and Victory Points to move the slider several points. The most drastic options can backfire, but as you can only use one option every 6 months, if you play safe you won't move the scale much. Basically if the CSA want to have a chance to get the British, they must risk something. And if they succeed, the USA can be obliged to escalate and risk also playing with some options.
As for the second point, if the Entry is positive, then there is a chance every 3 months to get some subsidies from Great Britain, so this is not only an On/Off affair. Even if the Confederate don't manage to get a military action, they can get some underground money from Europe.