M.S.
Check w/ Dr first.
I'd work on covering up before applying sunscreen. Wide brimmed hat w/tie so she can't take it off. If you wear one too, she'll eventually keep it on. Rash guard over the swimsuit or buy one of the bodysuit ones. and take or buy an umbrella. Stay off the beach from 10 - 3 when the sun's the strongest.
check out the report on sunscreens at ewg.org. they did a report last summer and rate them on safety and effectiveness.
Stick w/zinc oxide or titanium dioxide for sunblock. They are physical sunblocks meaning they sit on the top of the skin and actually block the UVA/UVB. they also have a long history of use and are known to be relatively safe. Think of the white nosed lifeguard in the 60's and 70's - that was zinc oxide. Walgreens has a zinc oxide blend that's good. so does neutrogena.
Most of the cheaper sunscreens are chemical sunscreens. this means they actually react w/your skin to provide the protection - that's why the bottles say to put them on 30 minutes prior to exposure. These chemicals do not have near as long a history and their safety is not really known. Our daughter reacts to avobenzene - one of the most common chemical sunblocks.