If im understanding you right, if you use multiple snippets of same type and same params on a page without any parameters that differ from eachother will create a conflict between these two snippet calls.
What you need to do is that you will need to put a placeholder parameter into one of those two login snippets, e.g:
[[!Login?
&toPlaceholder=`anything`
]]
Placeholders with prefix set in the parameter:
[[%anything.username]]
[[+anything.recaptcha_html]]
Default placeholders by Login are:
[[%login.username]]
[[+login.recaptcha_html]]
..etc
Hope this helped you,
-bow