Birds will sometimes make their nests in places that seem strange to you. When there are baby birds involved, you can also be uncertain of what to do about that. No, it is not a good idea to move a bird's nest with baby birds in it.
Birds are content in their nests. Birds will often return every season to the same spot to create a nest.
If you notice a nest in your yard and it is in an inconvenient place, try to avoid that area until the birds have vacated that nest. Baby birds do not typically stay in their nests for long. It takes about a month for the baby birds to be ready to leave it. Before you know it, you will be able to use that area of your yard again.
Sometimes, you might wonder if you should move the nest to a safer or more convenient place. This idea really is not recommended because there is the likelihood that the mother will abandon the nest.
When a mother bird makes a nest, it is not just the nest that the bird gets used to but the surroundings of it as well. If you move the nest, the bird might not be able to find it because its surroundings are different.
Avoid any activity around the nest with baby birds until they have vacated the area. The less activity in the nesting area, the safer it will be for the baby birds. The nest may be moved after it has been vacated.