Right, you had a (quick) question. The short answer is that if the other blog owner has been using "frugal adventures" as her blog title for longer than you (and that looks to be the case) then she's in a better position to stop your use. It's not likely to matter whether "frugal adventures" is prefaced by "my" or "our" (nor will it matter much that your blog is more family oriented). What's important is that both blogs have similar titles and deal with personal finance and saving money.
Will the other blog owner prevail? This isn't to say that the other blog owner will prevail against you in a legal battle. (Here are some of the trademark rules.) The other blog would have to prove that "frugal adventure" is protectable as a trademark -- that is, it's not descriptive of the services. If it is descriptive she will have to demonstrate consumers associate her name with those services. That may not be hard for her to do -- based on Google rankings, her blog appears to be more popular -- but even if she does prove it, she will also need to prove that there is a likelihood consumers will be confused between the two of you. Apparently neither of you has registered the mark with the USPTO.
Should you change? Like we said, assuming she was first, things look better for her than for you. If she has a lot invested in her blog's success, she may hire an attorney to keep her domain control. In that case, you'd have to decide whether you want the expense and hassle of dealing with it even if you did prevail. If your readers are regulars, it won't matter much if you change the title (or re-direct the domain name). Should you decide to change, we recommend searching out any future names to prevent such conflicts.