After 10 days of rest and seclusion, President Carter ended his spring vacation today and headed back to the problems awaiting him in Washington.

Carter and members of his family attended services here this morning during which his youngest grandchild, Sarah Rosemary, was "dedicated" in the Baptist Church.

The smiling president emerged from the church holding the 4-month-old child - daughter of his son, Jack, and daughter-in-law, Judy - and happily posed for pictures. But as has been the case since he left Washington on vacation April 12, he had nothing to say on substantive issues.

Carter planned his vacation that way, spending that first eight days of it on Sapelo, a secluded, almost inaccessible island off the Georgia coast, where fishing, reading and resting occupied most of his time. He also visited his home in Plains, Ga., for one day before flying here for what amounted to a family reunion.

In Plains, the president told reporters he had worked two or three hours a day on the island, mostly keeping informed on developments abroad and handling routine paperwork. He said what he enjoyed most about the vacation was the chance to "be alone."

The Carters reached the White House late this afternoon.

Beginning Monday, Carter will plunge back into the duties of his office. He has scheduled a Cabinet meeting in the morning and a speech in the afternoon to the National Academy of Sciences.

White House officials have also scheduled on Monday a briefing for reporters on the negotiations for a strategic arms limitation treaty (SALT) with the Soviet Union. The timing of the briefing is one of several signs that the administration expects to be able to announce agreement on SALT II very soon.

On Wednesday, the president will fly to New York, where he will address a convention of the American Newspaper Publishers Association, and then to New Hampshire for a "town meeting" and a political dinner.

New Hampshire, site of the nation's first presidential primary, is crucial to Carter's reelection chances. White House officials have also announced that on May 4 and 5 the president will visit Iowa and California, two other key states in the primary process.

In most of his appearances, the chief executive is expected to appeal to the public for support of a "windfall profits" tax on the oil industry, an issue White House officials clearly hope will help revive the "populist" image that served Carter so well in his 1976 campaign. CAPTION: Picture, Paternal Grandfather adjusts the bib of Sarah Rosemary Carter after her Baptist "dedication" ceremony. AP