Both
We all are planning to attend this party.
and
We are all planning to attend this party.
work.
For the extended sentence, some context is needed.
We all, with (or "and") other invited guests, are planning to attend this party.
would be fine if "We all" referred to a group that the person this sentence is spoken towards knows as a group (otherwise the 'we' does not work), and some other persons were also coming specifically with this group
We all and another invited person are planning to attend this party.
Would be fine if just one other person went with that one group specifically (the whole party my be attended by more people).
Just to be sure: If the 'other' invited guests referred to the (implicitly or explicitly) invited spouses of the guests,
We all, and our plus-ones, are planning to attend this party.
would be ok.