I'm sure there will be others who will be able to give a better answer to those specific questions about the Texas Coast than I, but I can not resist making some "non-specific" comments.
In April, the Hill Country of Central Texas is not to be missed. One cannot predict about whether this will be a great year for Bluebonnets, but most years are at least worth seeing. If you are along the coast, maybe you could slip up to San Antonio and then on up to Fredericksburg and Kerrville. (Just don't go through Austin. I have always found that a traffic nightmare.)
Another place I will mention is Choke Canyon State Park. We usually stop there on our way to "The Valley" (Texas Rio Grande Valley) and see plentiful wildlife.
All of these I have mentioned are quite a bit inland. The reason I leave it to others to make suggestions about the coast is that we have not usually followed that route.
I will mention only two of the places we have stayed that would be considered coastal: Sea Wind RV Resort near Riviera, Texas and the very large Breckenridge Plantation Recreation Area near Edna, Texas. I'd surely go back to either of those.
Welcome to Texas, wish you would be able to visit North East Texas and the Hill Country in the Springtime. But I know you can't do it all on one trip.