"In a sense the father is the priest of the household, laying upon the family altar the morning and evening sacrifice. But the wife and children should unite in prayer and join in the song of praise. In the morning before he leaves home for his daily labor, let the father gather his children about him and, bowing before God, commit them to the care of the Father in heaven. When the cares of the day are past, let the family unite in offering grateful prayer and raising the song of praise, in acknowledgment of divine care during the day. MH 392.2"
"Enter into his gates with thanksgiving, and into his courts with praise: be thankful unto him, and bless his name."
Both passages encourage praise and thanksgiving in worship. The EGW passage describes family worship with prayer and song, while Psalm 100:4 is a general call to enter God's presence with thanksgiving and praise. The connection is valid and meaningful.
"And if it seem evil unto you to serve the Lord, choose you this day whom ye will serve; whether the gods which your fathers served that were on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the Lord."
Both passages emphasize family worship and commitment to serving God within the household. Joshua 24:15 is a declaration of intent, while the EGW passage describes a practice that embodies that intent. The connection is present, but not overly strong.