Hi there - yes, that’s a good interpretation and, to me, an accurate understanding. If it helps, you can think of share like a portion or piece or “amount of something” that is available to take or receive. For example, if your mom made a cake and you and your brother wanted to eat it, she might instruct each of you to eat/take/receive your share of the cake. The share doesn’t necessarily have to be equal in amount, it just needs to add up to a whole (or 100%). So, for example, if you were 10 years old, but your brother was 2 years old, it is like that your portion cake will be larger than his because of your capacity to eat more cake for possibly several reasons. But, mainly because you are older and can eat more than him physically. You both still have your specific share according to each of your capacities, but they might be different.
For the word “blame”, I think responsibility is a good word, or at least a great understanding of what the phrase is trying to communicate. You could also think of “blame” in this instance as “accountability”. So, another example: you and your brother are playing. He starts tickling you and you start laughing so hard that you trip, accidentally knock over, and break your mom’s favorite flower vase. You didn’t mean to, but you were laughing so hard from your brother tickling you, you lost your balance and bumped into the bookcase the vase was on. But, when your mom is upset and asks what happened, you blame your brother because he tickled you and made you laugh so hard. In this instance, you are not “taking your share of the blame” or holding yourself accountable for the fact that you also were a part of the circumstances or story of how the vase was broken, even if it was an accident.
Very long but I think you have the right idea. I hope this maybe gives a bit kore context/examples in which to consider the phrase.