Yeah, that's exactly how these spells are supposed to work.
But before you call it overpowered, let them try it out at least once. It uses up both the Druid's 3rd level spell slots (assuming they have enough Wis to even have 2 slots) and requires 2 actions to set up, while creatures will start trying to leave the entangled area after the first one already. Also, most combats don't last more than 3-4 rounds, so by the time this effect is fully active, the battle is probably half over anyway. And it only works outside.
It might be very powerful, but that'd be pretty situational, which is generally fine; let the Druid shine in those situations. In the average dungeon, this combo doesn't work anyway, in the average outside combat it probably won't deal more damage than 2 Fireballs, and the Fireballs will grow even more powerful in the coming few levels, while this combo doesn't.
Use the limitations of Travel via Plants to your advantage.
Secrecy is the first and best line of defense.
The rules for Transport via Plants suggest that you can only select a specific destination plant if it is familiar to you. Otherwise, you must specify desired distance and direction and the spell will transport you to the nearest plant of the same type as the origin plant to the location you specify.
If you are uncertain of the location of a particular kind of destination plant, you need merely designate direction and distance and the transport via plants spell moves you as close as possible to the desired location.
So the invading druid would need one of two pieces of information. First they would need to be familiar with a specific plant inside the target grove. Failing that, they would have to have enough of an idea where the target grove is that they could specify distance and direction and jump to the nearest similar plant. With this in mind, the best way to keep other druids out is to prevent them from becoming familiar with the plants there or prevent them from knowing the location. So: operational security; keep a tight hold on information.
Populate your grove entirely with plants that are tiny in size or smaller.
Transport vis Plants states that "You can enter any normal plant (equal to your size or larger)" (emphasis added). If all the plants in your grove are tiny or smaller in size, then no Small or Medium (or larger) druids can transport there. A tiny druid could still pull it off, but this guards against the main character races if they don't use magical size reduction.
Populate your grove entirely with plant creatures instead of normal plants.
This rather extreme option takes advantage of the fact that "You can't use [Transport via Plants] to travel through plant creatures."
If possible, populate your grove only with unique or extremely rare plants.
If you can have a grove with unique plants that don't exist elsewhere, or a type of plant that is prohibitively difficult to find, you can preclude another druid from getting there with Transport via Plants since they need a plant of the same type to travel.
Best Answer
Plant Growth
Land's Stride
Well then, this one is a little tricky. First and most importantly, "Plant Growth" does not actually create Difficult Terrain with its spell effect, nor does it create magical plants, vines, thorns, etc. It does, however, cause naturally occuring plants to become so overgrown that it impedes or otherwise slows anyone moving through the area, with a magical effect.
When we look at Land's Stride we see that moving through nonmagical difficult terrain will costs you no extra movement. Since this is not difficult terrain, however, this first part does not apply when you move through the effected area of Plant Growth. Then we see that "You can also pass through nonmagical plants without being slowed" , which is where the synergy comes in to play. Since Plant Growth uses magic to cause mundane nonmagical plants and vegetation to overgrow and effect your movement, Land's Stride allows you to move through these plants without being affected. Lastly, since 'Plant Growth' does not offer you a saving throw for you to have Advantage against, the last part of Land's Stride also does not apply here, but it IS important to note that "plants that are magically manipulated to impede movement" is precisely what Plant Growth is doing, even if the plants themselves are nonmagical in nature.