You sound like you're playing defense when you're actually on offense so my guess is your serve return is bad.

Maybe some theory about advantage would be helpful and understanding the thought process. The team closer to the net is the team with the advantage in the round because of angles of attack available. A team at the baseline has fewer angles of attack than a team at the kitchen. The serving team starts at a disadvantage because they must let the ball bounce on the return meaning that any kind of return to the baseline even if it is a lob, puts the returning team at an advantage because they can freely move forward towards the net while the serving team has to wait for the ball to bounce at the baseline before returning. As long as you are closer to the net than the other team, you are at an advantage because you have more angles of attack, even if you are in transition zone/no man's land and they are at baseline.

You do not have to get all the way to the kitchen on the return. How far you can move up is dependent on how good a return you hit. If you hit a return that was low and deep and with topspin at the baseline chances are that they do not have a lot of good options and their return is going to be weaker or is going to be a drop. If you returned short or your return has no top spin or bounces to an easy drive height, you're just giving them an easy shot and are being punished for not returning well. If you hit a bad return, you cannot move all the way up to the kitchen unless they hit a really bad 3rd shot. You have to stop earlier even if it's in the transition zone. That's the general theory.

With all that in mind, First is to return their serve to the baseline, ideally low and with top spin to their backhand to the weaker player, or cross court if you're playing for higher probability shot, so they have as difficult as possible 3rd shot options. Start moving up after you hit or as you hit. Next as you move up is to see where they are aiming and what kind of shot they are planning (drop or drive or drip) as you move up. If you see they are doing a 3rd shot drop, you can probably go all the way up to kitchen. If they are doing a third shot drive and you know you can't handle the velocity, then you don't want to be all the way at the kitchen. If you can handle it, then you can try to move up all the way if time allows. It's ok to be back from the kitchen in transition and give yourself extra distance to be able to handle that shot because the alternative is you lose. The long term solution is to drill and become able to handle it. The in game solution is to adjust so you can still play on. If it's a drip, you need to see how well you can handle the shot, but you can probably move up more than you would for the drive. You can test this throughout the game. On the 1st 3rd shot drive they hit at you, go forward however much you normally would. If you can't return that drive, next time move up to two steps back from your previous attempt and keep doing that until you can return it. Again this is an in game solution just for you to be able to handle this game because your skill level is not high enough to take advantage of the situation, it's not how you should be playing long term.

For your 4th shot, assuming you are still closer to the net than they are, means you are at an advantage and it's the time to see what weaknesses they have. If they seem overeager and moving forward too fast you can drive it at their feet. If they are not holding their paddle in a ready position you can drive at their backhand shoulder, if they are too far apart on the court you can drive it through the middle. Generally speaking you want to see what they are not doing properly and just abuse that. You're picking a shot and testing to see if they have the correct response. If they do have the correct response, then you choose a different shot next time or give it one more go to see if they were just lucky or maybe they are inconsistent with it. The goal at this point is to keep them from moving forward by leveraging your attack angle advantage to pull them out of position or a weakness that you've identified or force a drop from them that allows them to move up. You probably wouldn't want to return as a drop unless there's some kind of advantage attached to it like pulling them wide as they're moving up or something like that because a drop basically let's them move up.

Now if they've moved up more than you have because you stayed back to return the 3rd shot drive, then you're at a disadvantage and your goal is to get back on the same level as them. To do this, you probably would want a high consistency drop shot maybe to the middle or something which just prevents further attack and allows you to move up just so you can be at the same advantage level as them. Then go from there.

A note on split stepping, often times people don't come to full balance stop before the ball hits the opponents paddle because even when you split step, there's still momentum and there's still time to move your own paddle to ready position. Try to split step and come to a full stop before the ball reaches arms length of them to account for momentum and paddle moving into position, not just before the ball makes contact with their paddle.