Here is what I have found in my research:
If a private person wishes to build a chapel or set a room aside for the reservation of the Blessed Sacrament, they will need:
-The approval of the local ordinary
-A bishop or an agent sent on his authority needs to inspect that the place is suitable for sacred worship and is in compliance with the norms for liturgical function
-The chapel should be blessed or consecrated to the exclusive use of sacred worship (I do not think it has to be blessed exclusively by a bishop, I understand even a deacon could do so. Consecration would most definitely be done by a bishop.)
-If the place reverts to secular use, they will again, need the permission of the local ordinary to do so
-Mass must be celebrated at least twice a month to tie in the presence of the Eucharist with the liturgical action
If a person wishes to set aside a room or build a chapel,
without the reservation of the Blessed Sacrament:
-he needs no approval
-he could have the place blessed, as long as the space is completely set aside exclusively for sacred worship
-he would need approval for Mass to be celebrated there
More than that I do not know, which is why I suggest the best thing the OP to do would be:
-pray
-lay out plans with an architect
-if you intend to have Mass said regularly, you may wish to find a priest who would be willing to do it. I would contact a religious order you are close to, or try calling a retirement home for priests, to see if there are any available to say Mass, if everything is approved.
-find out what city permits are needed, etc…
-make an appointment with the bishop of the diocese in which he intends to build
-bring the architect plans and building code permits, etc…
-discuss the beautiful custom of your family
-tell him of your desire and why you want to build the chapel and show him the architect’s plans
If he approves:
-find out what needs to happen next
-do some reading on your own about chapels. For instance, it is the norm that chapels be blessed, but I would want mine consecrated by a bishop. Another issue for me is that I want to have Mass in the Extraordinary Form. That takes more planning, consecration of the altar, making sure I have all of the correct altar gear, vestments and objects needed.
-you may need to coordinate a meeting between a knowledgeable priest and an architect.
The fun part will be designing your chapel. I’d love to see your plans and hear what ideas you have. I have been pulling ideas for altars, interior and exterior shape, choir loft, seating, color scheme, windows, ceiling paintings, flooring, vestibule and sacristy and other interior and exterior features and details.
The first thing I did, was to decided which saint or event of Christ’s life I would dedicate the chapel to. That gave me a “theme,” so to speak, which I could work the design around. Search the internet or visit chapels and find elements that you like and think would work well together. Take the ideas to your architect and have him/her bring your ideas together.
A few architectural firms I would recommend:
mccreryarchitects.com/
cramandferguson.com/
stjudeliturgicalarts.com/
georgiangroup.org.uk/docs/awards/winners.php?id=4:52:0:5
Please keep us informed as to how things progress.