You will never match the quality of the existing tile work unless you pay a high premium for a tile specialist instead of a regular remodel job. Removing that tile will cause a big mess and a large bill for demo and disposal for no real advantage. The current surfaces are durable, not offensive and easy to clean and those are important attributes when you have one or more youngsters in your home.
I wouldn't bother with reglazing the tub until your children are older. The new surface will require more careful cleaning than the existing tub
Q