If this is a "long" term arrangement, that your Relative will be caring for her...then I would definitely get a crib or pack n' play for when your baby is at their home.
The reason being... that way you can keep her sleep/nap "habits" consistent... and then there won't be a big change in that compared to her home environment. It is therefore an "investment"... to ensure your baby's consistent habits.
Beware... that any "new" sleep/nap habits she acquires at her Relative... MAY interfere/abrupt her sleep/nap habits at home.... and being that you JUST got her to sleeping in her crib nicely... I would not want to mess with that...otherwise you may have trouble getting her to sleep at home too.
Being that this is a Relative caring for your baby... just "duplicate" your nap/sleep routine for her there as well. Tell your relative "how" the routine goes. Write it down if you have to. This is what I do, when Grandma babysits my son. The reason being, if the routine is "different"....my son will NOT nap. And then he gets into bad habits... which I therefore have to "correct" after Grandma. And this takes time, to get them back to their original "routine." And, it's not fun. Mommy suffers the backlash of "bad" habits learned by Grandma...although well intentioned.
So, if your relative gets your baby into the "habit" of being rocked, carried, or co-slept with, in order for her to nap/sleep.... your baby will then expect this at home too. So you need to think IF this is a "new" habit that you want to continue at home, or not.
Many times, when a baby/child's routine is changed...it may probably change their habit at home too.
Just keep that in mind.
My vote is to (1) get a crib/pack n' play for the relative (2) have them keep to your nap/sleep routine that you have for your baby and "duplicate" it...thus, keeping consistency when she is at home too, and she won't get "confused" as to how to fall asleep.
All the best,
Susan