He will tell you it is only a bit of caulk. You will look at the line where the tub meets the tile and see black, a gap you could slide a fingernail into, and one corner that has pulled away from the wall. You are both partly right, and that is the trouble. Old sealant is a simple job. Water getting behind it is not.
Local option: New Plan Care gives families in the St. Louis area in-home help so a parent can stay home: companionship, help with bathing and dressing, meals, and overnight care. Call (314) 405-0887.
What to check before anyone buys a tube
Press along the seam with your thumb, gently. If the old bead is hard, cracked, or peels off in strips, that is age and damp, and most people can redo it in an afternoon. If the wall or the tile gives under your thumb, or the grout behind the joint crumbles, stop there. The caulk is only the symptom, and the fix is in what it sits on.
Look at the black itself. If it wipes off with a scrub and the seam is tight, it is surface mildew on sound sealant. If it sits in a line inside a gap, or the paint on the wall above the corner is bubbled or stained, water has been getting in and staying. Check the bottom edge too, where the tub meets the floor. A line of dark swelling there means the floor may be taking the water.
Stand at the edge of the tub, not in it, and rock your weight slightly. If the tub flexes or the seam opens under you, new caulk cannot hold a moving joint. That is a question for someone who knows tubs and walls, not for a weekend.
Do it yourself when
The seam is a single straight run, the wall behind it feels firm, the corner is closed tight, and you can keep the room dry for a full day while the sealant cures. Read the label on the tube before you buy it. You want a sealant made for wet areas and tub joints, and you want to know the cure time before the next shower. Ask the person at the counter which one suits a bathroom seam. Do not run water on it until the cure time has passed, and do not trust the feel of the surface as a sign it is ready.
Hire it out when
The corner is open, the wall or floor is soft, the grout is loose for more than a foot, or the tub moves. Ask the person who comes to look three things. Will you pull out all the old caulk, or lay new over the top? Caulk over old caulk fails within a season, and you will be paying twice. What will you do if you find soft board behind the tile, and who pays for that if it turns up? Will the work be guaranteed in writing, and for how long?
Compare two quotes by the steps, not the total. Each one should list removing the old seal, cleaning and drying the joint, taping, sealing, smoothing, and curing, plus anything found behind the wall. If one quote skips a step, the cheaper number is not a bargain.
Tonight
Lay a folded towel along the tub edge so water does not sit on the seam, and ask him to hold off on the long hot showers until someone has looked at it. Take a photo of the corner with the light coming from the side, so whoever comes next can see what changed. Put the tube and the box it came in in the same drawer, so you both know where the answer is.
When to ask the doctor
If he has slipped at the tub edge, or he has started reaching for the wall or the towel bar to steady himself, mention it at his next visit. A tub seam is a house problem, but a wobble at the tub edge is worth saying out loud to the person who looks after his health.
Good-week card
The seam is dry, the towel is back on its hook, and you both know which of you made the call.