Sub-questions:

Do Suggestion's suggested activities need to be pursued immediately, at the expense of anything else?

Can the DM decide that the influence of Suggestion sets limits on action economy, like some conditions?

My scenario:

I'm a player. Party is surprised by a group of enemies. I'm on watch outside, rest of the party's inside asleep. After being hit with three arrows and yelling the party awake, I fail the check against the caster's Suggestion, who says "you've been invited to meet our leader, accept the invitation and come with me to the palace." Being a loyal group-oriented type, my character asks if he can bring his friends. Caster says yes. Meanwhile, baddies are laying into the folks inside pretty hard, some of which I can see.

Now, I'm into it and ready to role-play trying to get the party to leave with our "escorts", but when my turn comes, DM says that I cannot take any actions or move in any direction other than towards the palace (wherever that is) or to get within 5ft of the caster (who is already next to me). Instead I must hold an action to Dash towards the caster if she moves, apparently because she said "come with me." What I think my character understood from her words (i.e. that we were getting ready for a trip together) and how they would pursue it (go in to break up camp, admonish my imperiled friends for dallying), does not sway DM, who calls this a "judgement call."

This kinda killed the session for me, and it continues to irk me for a few reasons:

1. As a player I totally rolled with a borderline unreasonable suggestion (i.e. stop fighting and cooperate with people who pincushioned me seconds before and were actively firing on my allies), had a character-specific plan for pursuing it, and was denied the opportunity to role-play;

2. The idea that "come with me to the palace" means "cleave to my side and do nothing else" doesn't sit right with me (is it normal to stick right next to your companions, even when they aren't leaving yet?), especially after my character got permission to bring a friend.

3. I have just never encountered Suggestion being used this way – as in, having a specific mechanical effect with consequences for action economy like the Command spell or Fear does, and there's no language about it in the spell as written.

Now, there is the "rule of fun" which was obviously broken for me, but there is also the more objective question of the actual rules of the spell, and it seems to come down to a lack of clarity on who gets to decide how a Suggestion is resolved. I've found a lot of discussion on what's a "reasonable" suggestion to begin with, but no satisfying answers on this part. When PCs cast on NPCs, DM obviously decides NPC's interpretation and any behavior that isn't made explicit by the PC, but what about the other way around?

I get preventing players from specifically subverting the suggestion or delaying it too long, but this seemed absurd. What if I had left all my weapons and money inside, could I not go fetch them? What if some gnolls attacked on the way there? Should I not take any attack actions then? In combat, even if a player's whole turn should be used with the suggestion as the main goal, should the player still get to select an action/movement that they think achieves it (and therefore possibly go get the money or kill the gnolls blocking the way)?

And can a player supply their character's interpretation of the Suggestion, provided they do so in good faith? I know there's a degree of DM discretion in all things, but this scenario seemed to me like a straight-up wrong interpretation of the spell and I would like to know if this is the case or if it really is just a judgement call.