How to handle marital gifts

This is easy. If you received gifts for or after your marriage, these gifts belong to both you and your spouse equally, unless the third party who bestowed the gift made it clear that the gift was for only one of the spouses. Absent a showing that the gift was intended to be for only one spouse (rebuttable presumption test) then the gift, if given during marriage is marital and belongs to both parties. In other words, they are sort of “joint” gifts.
If the spouses give gifts to each other during marriage, the gifts are marital property. Gifts can even be joint bank accounts where only one spouse makes deposits with their own funds. The law usually interprets the joint account as being half owned by the other spouse due to a “gift” of one half being given by the spouse who opened the account. But again, there is a “rebuttable presumption” that this was not the intent.
So if you get divorced, you will have to split the proceeds with your spouse unless the spouse can show that it was not intended to be jointly owned. Or you can do a trade off with something else as long as you both end up with equivalent value.  Or your spouse or you may decide to forego electing to get a share of the gifts. Whatever. But if the gifts are “marital” meaning that you either received them for your marriage, or during your marriage, they belong to both spouses.
The exception would be inheritances, and, as I said before, gifts given by third parties to only one spouse. Also, some gifts are conditional gifts, like the engagement ring. The engagement ring could be deemed a marital gift depending on the value of it, otherwise it is “separate property.” 
But, yes. If one spouse receives an inheritance during marriage, it is not marital property, unless an intent can be shown by the other spouse, that it was intended to be marital property. Same for gifts by third parties which were not intended to be for both spouses. Any gift that is “separate” property would belong to the spouse who has ownership or title only, and it would not be put in the marital “pot” to be distributed if there is a divorce.