>could it effect their motion in their favor?
You need specific grounds for a restraining order. The bare minimum is reasonable fear of emotional abuse.
So, if you are not going to argue that your already poor health is being threatened by the other party, then that's not at issue, so it can't affect the judge's decision in the other hearing.
Howver, if the opposite is true, and the judge rules that your health was a factor in issuing the restraining order, then that's a fact that the judge must consider as already determined in the custody hearing.
Moreover, if the continuance was granted on grounds that your health was compromised, then the other party already has a ruling that it can use against you. I'm guessing, based on your facts, that the judge used the conflicting "federal" case (which by-the-way is impossible -- state courts don't hear federal cases -- so I don't really know what the judge's continuance was based on), as the basis for the ruling, and judges rarely explain their reasons for granting a continuance, so, I don't think the continuance will be useful to the other party.
But, the restraining order could be. Hard to tell.