It could be both, I guess.
If you say, “I have to bring the kids up and once they’re 18, I’ll finally be free again.” then it’s a means goal because you feel you have to do it so that you can be free again.
But usually parenting is an end goal. It has meaning in it. You do it for the sake of doing it and not for reaching somewhere. Your goal might be “I want to be the best mom I can be.” or “I want to be in love with my kids every day.”
You’re right. Parenting is different. You get happiness from meaning, but in the moment as a parent you’re maybe not always happy. Roy Baumeister calls this the “parenting paradox.” Parenting is highly meaningful, even though it’s also highly demanding and requires personal sacrifices that go agains short-term happiness. Basically, we humans find meaning so important that we’ll sacrifice a certain amount of happiness for it.
I’m no parent yet, but I’m sure even though parenting is demanding, you wouldn’t want to trade it for anything.
Anchoring one’s happiness to that of others might not be the best idea. You can only do your best and you cannot control your kids’ actions and everything. I’d say you want to give your best at parenting and give love and affection to each child, but you don’t anchor your happiness to it. In the end you don’t control everything that happens.