It is not necessarily a crime to do this, but the gift to you and from you to Betty would be disregarded and treated as if gift directly from Alice to Betty, if the IRS knew all of the facts. A gift implies a donative intent directed at you. When there is an understanding that you are acting at Alice's direction, you aren't receiving a gift, you are acting as Alice's agent.
This said, this scheme, or the alternative it seeks to prevent, has no impact on Betty, because gift taxes are imposed on the donor rather than the recipient of the gift. And, in most cases, a gift in excess of the $14,000 per person per year gift tax exemption will have only a minimal impact. This is because each person is entitled to make a combination of gifts in excess of the exemption during life and transfers to non-spouses and non-charities at death of $11,200,000 per lifetime (adjusted annually for inflation).
Usually, all that is necessary if the limit is exceeded is for the donor to file form 706 (a federal gift tax return) at the same time as the donor's income tax return, and this form is very simple if the only gifts given are cash gifts.
Transfers to a U.S. citizen spouse are gift and estate tax free, as are gifts to foreign and domestic charities.
Spouses who file a Form 709 in a year may treat gifts given by one spouse as actually given half by each spouse.
If someone dies not having used their entire $11,200,000 (adjusted for inflation) lifetime exemption, their surviving spouse, if any, inherits that unused portion and can use it at their death in addition to their own lifetime exemption.
So, Alice and Betty are trying to evade a tax law that is easy and trouble free to comply with, and may provide future benefits by documenting the intent of the parties with respect to a large gift (so that someone doesn't later try to characterize it as a loan or contribution to a trust estate, for example).
While it isn't a crime, it is ill advised and won't benefit them materially in the end.