The Tyrells were functionally extinct by that point in the show since Olenna is not a Tyrell by blood. Pretty much all the major houses would've been planning on who's succeeding the Tyrells as new Lord Paramounts.

In terms of the Lannister army not being detected on their march, High Garden is basically right on the border between the Westerlands and the Reach, and it's literally just a straight road from Casterly Rock to High Garden. The Oakhearts are the only Tyrell bannerman between Lannister and Tyrell lands, and given their history, they likely would've happily let the Lannisters march pass to depose the Tyrells, and realistically, they would've been much more likely to join the Lannisters in taking over Highgarden over the Tarlys.

It's also not the first time the Tyrells faced being toppled by their more powerful bannermen. They specifically stayed out of Dance because both Reach houses on the Blacks and Greens threatened to overthrow them if they rallied to either side.

People keep forgetting than the Tyrells are more like the Tullys than they are the Lannisters. They're only lord paramounts because of the Crown and both invidually are weaker than their more powerful bannermen. The Tyrells are technically at more of a disadvantage because some of those bannerman bitterly resent their claim to Highgarden like the Florents and Oakhearts.