I would like to recommend a carrier carseat, base and snap n go combo. Even if you plan to get your little girl out each time and "wear" her in a carrier or hold her, there are many times it's nice to have a carrier she can continue a nap in, or to transport her through a store. If you're looking for something for multiple cars, I recommend multiple bases to snap the carseat into.
I do think a convertible carseat is a great idea for when she outgrows the carrier (usually 29 inches or 22 lbs).
For carrier seats I have had great experiences with both evenflo and graco brands. For convertible carseats I have used evenflo (the straps don't go high enough my just barely 3 year old is almost too tall), alpha omega and the cheapest brand at walmart (for my husband's car, works great).
How far is your mom? We bring carseats with us when we travel. Manufacturers recommend carseats be replaced every 6 years for safety reasons, so our parents have not purchased carseats, we just take them with us on trips.