UA is offering a +/- 1-day change. But, OP is also entitled to cancel for a full refund without penalty. He may then purchase whatever ticket he wants on whatever carrier he wants. If UG's are available, he can UG.

Either UA shows OP as having accepted the proposed rebook and is now giving him a hard time about a second fee-free change or it is simpler to cancel for a refund. OP may also want to consider that it may be cheaper to cancel and rebook.