These kinds of projects are rarely easy and usually take a lot of time to get right. But, in my 15 minutes of research, I think it's doable. There are some questions that need answering first before you consider moving:
1. What features is she currently using? How important is each feature? Does any one feature absolutely have to be there? Are there any deal breakers if the feature isn't there? For example, email integration probably isn't as important as actually tracking customers.
To figure this out, you will need to walk though the entire daylite app and decide what absolutely has to stay and what can be omitted. Once you have this feature list established, you can move to step 2.
2. Moving the data: this doesn't look to be impossible, but will require patience and effort. It looks like daylite allows exporting via CSV. This is good because CSV is pretty easy to import to most systems. Does your new system support CSV import? Can you export all the data you need from daylite to CSV? If not, how much manual recreation will there be?
3. Playing well with others: are there multiple users who use this CRM? Is there a server? If so, what will the new server look like? Where will it be hosted and who will maintain it? These are costs that will be ongoing.
4. Picking a new solution: This part is the hardest, but is informed by evaluating the previous questions. You need the ability to import directly from daylite or via CSV. Once the data is transferred, you will want the ability to export it if you choose to change CRMs again in the future. In the best case scenario you'll have multiple solutions providers to pick from. In reality, it will probably be a few that have most of the features you want. In evaluating an open source solution, you'll want to make sure there is both ongoing support available and a community which will help to support you and the application going forward. Research here is your best friend.
EDIT: 5. User training. This is something that I did forget. You're going to have to train the users on the new system. This takes time and effort.
There's probably more to consider that I am omitting.
In any case, you need two things: 1. A use case study to figure out what the software is doing now. 2. A plan to move from the current solution to a new solution. Your mom should probably contact an MSP or a specialist if this dataset is of any size or importance.