yes, of course, you can
what you will probably have to do is,
get a letter from your employer,
get hotel and flight booking of your parent.
show good bank balance over the period,
you must have valid J1 visa left for quite a good 6 months or more time
your J1 2019 form
all those help and is more then engough , go ahead and start doing it.
please do take some professional advice before doing anything else
amin