Unless this letter came from an attorney demanding a change AND the other site was there first she probably does not need to.
If a an attorney's C&D letter comes, she had better speak with a trademark attorney b/c his stuff can get complex and non-intuitive.
Information here is general, does not create a lawyer-client relationship, nor a substitute for consulting with an experienced attorney on the specifics of your situation.
My initial impression is that your wife registered the domain name in good faith and has a legitimate interest in using the domain name for her blog, so this does not sound like a case of cybersquatting.
However, there may be a trademark infringement issue if there is a likelihood of confusion between the two. This would require consideration of specific facts such as each party's prior use of the mark, the similarity of the marks, the similarity of the goods and services, etc.
If you receive a letter from their attorney threatening a UDRP action, or a claim under 15 U.S.C. § 1125(d), also know as the Anticybersquatting Consumer Protection Act or ACPA, or another legal claim such as trademark infringement, you should consult with an attorney (preferably one with trademark experience).
This answer is for informational purposes only. It is not intended as specific legal advice regarding your question. The answer could be different if all of the facts were known. This answer does not establish an attorney-client relationship.
I agree with my colleagues and would add one more consideration. A domain name is like a phone number or address - it's just a location on the internet. There are no trademark rights in the domain name itself. The trademark rights in a domain name have to accrue from use of the domain name like a trademark. In other words, that domain name has to function as an identifier of the source of the service. Your wife's blog cannot merely be located on that domain name; the domain name must be used as the title of the blog or in some prominent manner that identifies the blog as coming from your wife and not someone else.
Other rules of trademark infringement also apply if that is what is being alleged. For instance, the word being shared and allegedly causing consumer confusion cannot be descriptive of the services and the goods/services for each of you must be in the same channels of trade. If the blog is about issues encountered by moms, there may not be any trademark rights because the wording is not a source-identifier for the blog. If the accuser operates as part of a TV show and your wife's content is completely unrelated to that and targets a different audience, there should not be any trademark infringement.
If you have specific correspondence from a lawyer or threatening legal action, you need to consult a lawyer promptly to address it and it could very well be defensible without a significant cost. But if it is simply a threat from the website host, you might be able to ignore it for now.
Alex Butterman is a trademark attorney with Staas& Halsey LLP (http://www.staasandhalsey.com), a Washington, D.C. IP boutique law firm. Alex is admitted to the bars of Washington, D.C., New York and New Jersey but, unless otherwise specified, the answer is intended to be general enough to apply to any U.S. state and based primarily upon his knowledge and experience with applicable federal laws. The opinions expressed are those of the author and do not necessarily reflect the views of his firm, Avvo or other attorneys. This answer is for general information purposes only and is not intended to be and should not be taken as legal advice. No attoreny-client relationship or obligations are established herein, although consulting an attorney to discuss your specific situation is strongly recommended. This is especially true of trademark law and probably any area of intellectual property law because TM law is so fact-specific and full of esoteric nuances and exceptions, that more often than not there does seem to be harm in handling a trademark matter without consulting an experienced trademark attorney.