This is really three related questions:
How to properly support and cooperate with our Royal Regency Council?
How to gain a stable and mutually beneficial relationship with our southern friends?
How to assure that our country has stable and competent leadership under these taxing times?
one, How to properly support and cooperate with our Royal Regency Council?
At theses taxing times the country needs stability and continuity. It needs a government it knows and can trust. Because of this you and the regency council need to start working together as soon and as intimately as possible. The members of regency council are after all chosen for their experience and dependability, who else could teach a young monarch how to do his work well enough to assure a smooth transition that does not give foreign powers a chance to interfere with our politics? And who could be a better candidate for being a minister in the future Royal Government than those of the Regency Council already proven to work well with their King?
Basically, if you flatter them, promise future positions in the government, and use their fear of "foreign power interference" to keep them meek, you'll probably be able to insert yourself into the decision making process of the regency council. And gather future allies instead of detached heads while doing it too.
two, How to gain a stable and mutually beneficial relationship with our southern friends?
You cannot stop your neighbour from conquering you and you do not have anything to offer them they cannot simply take. Except friendship. They can force you to be their allies in a war, they cannot force you to be their friends in peace.
You have to make the value of your friendship larger than the value of conquering or subjugating you. Then offer that friendship, not an alliance, you do not want to be entangled in their wars and problems, just a friendship, freely and without strings attached.
They have no shortage of conquest and an acute shortage of actual friends not allied to them, so finding some value should not be that hard.
The most important part is to understand that countries do not actually exist, they are just collections of people who have agreed to pretend the country really exists. Normally this can be ignored and it is considered polite to pretend the emperor is clothed in luxurious robes instead of prancing around naked.
But in a case such as this there getting leverage on the actual country is almost impossible, there is high value in accepting that getting leverage on the actual people making the decision about whether to invade you is what actually matters in addition to being much easier to do. We usually ignore this but personal interests have higher priority in decision making than national interests even if you are a leader of the nation in question. Good leaders will try to compensate for this but politicians are not generally very good at it beyond superficial level.
So go and talk with them. Learn them and how they think. And most importantly get them used to talking to you and being listened to. Be polite, respectful and attentive. Leave ass kissing to people who want to be allied with them. You want them to think that any opinion you choose to give them is based on an intelligent person who cares about them honestly thinking about it and giving it straight.
Basically, if there is a reason for them to invade you, you want to be told about it in a private discussion you are actually a participant of while you can still influence the decision. Not by tank divisions in the streets of your capital after the decision. Similarly being told about things you can do to help your friends in the south in private discussion has great value in making yourself valuable.
You need to make them want to talk to you and be friends with you. Your country is not important enough to make your objections matter, you have be a person whose opinions matter, if you want to influence whether they invade your country or not.
Find the people worth talking to and learn to express your thoughts in a way they listen to. The way something is expressed and by whom is lot more important than people think. The most important decision you want them to do is "Is this worth listening and thinking about?" and that is made before considering the facts.
You might want to bring them gifts so that they are happy to talk with you. Something thoughtful that cannot be seen as a bribe is best. A box of candy, some flowers, telling a story about something you know they are interested in, a chance to flirt with your pretty sister...
Something transient that puts them in a good receptive mood while they are talking with you and can then be forgotten apart from the general impression of a thoughtful person who is pleasant to meet.
For long term influence shared experiences and memories work better. Since you are the visitor, you want them to invite you. Getting those invitations is an useful metric of how good a job you are doing on the "friendship offensive".
Strategically the key points are to remember the objective, avoiding being conquered or subjugated, and to respond rapidly and effectively to any issues or opportunities in your relationship with the southern friends.
You must have good visibility to their decision making process. Make those personal connections and let official connections follow. It doesn't hurt to let people know that relations with the south are your primary concern. Make it clear upfront.
You must be in a position to respond instantly. Prudence is your friend. Try to predict what might happen and how you'd want to respond, in an unstable world both threats and opportunities will come. Avoid things that might cause problems later. Do not commit to anything that will restrict your options. Being a personal friend of their leader is great, being their formal ally is a chain dragging your country down.
You must make all decisions so they further your main goal. Everything is connected to everything else, if you for a moment imagine that some decision is not connected to protecting your country from invasion, then that decision will probably lead to increased chance of invasion later on. If nothing else the time you wasted on a decision anyone else could have made distracted you from achieving your goal. Just delegate everything else, okay?
three, How to assure that our country has stable and competent leadership under these taxing times?
The last goal is in some ways the easiest to achieve. If there is a real threat of invasion by far superior force and you are clearly and openly doing everything you can to prevent that, people will support you as long as you succeed. Happily, if you fail what people think no longer matters...
So the only thing you need to do in addition to the above is to talk to the people and tell them what you are doing and why. If your goal is keep the country safe from invasion that is what what people will evaluate you for. The situation gives you the ability yourself decide what people use to measure your success, which is something most politicians would kill for. So popular support should not be an issue.
Just remind the people of how strong and threatening our neighbours are regularly. Your friends in the south will probably be more than happy to publicly brag about how powerful they are and can help you a lot here.
This can be done indirectly. Modernizing the military, for example, is a nice opportunity to remind people how much better the weapons your neighbours have are. And how much more of them they have. And how much more experience their soldiers have using those weapons. And it is a nice opportunity for friendly cooperation with your friends in the south as well. Cooperation which happens because you personally have tirelessly worked to improve the relationship with them.
You should focus on that relationship and delegate everything else. This prevents any blame of failures elsewhere affecting you personally and allows you to use the inevitable failures to remove people you dislike and strengthen your position. Machiavelli has a famous example of how to do this. Be the one who fixes fails, not the one who commits them. Do not suppress the opposition, just let them fail and pounce.
You can game the system to increase the odds, as in Machiavelli, but even if you play fair counting on people to fail if given the opportunity is pretty much the safest bet you can make. And if by any chance somebody is too competent to fail, having a leading politician who does excessively good work is one of those "first world problems" you can usually live with.